% Upper-case    A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
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% Digits        0 1 2 3 4 5 6 7 8 9
% Exclamation   !           Double quote "          Hash (number) #
% Dollar        $           Percent      %          Ampersand     &
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% At            @           Left bracket [          Backslash     \
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% Right brace   }           Tilde        ~


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%

\newcommand{\gl}{Ginzburg--Landau }
\newcommand{\GL}{GINZBURG--LANDAU }
\newcommand{\g}{g}
\newcommand{\e}{e}
\newcommand{\esqr}{e^2}
\newcommand{\elm}{electromagnetic }
\newcommand{\f}{\frac}
\newcommand{\p}{\delta}
\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}
\newcommand{\beqn}{\begin{eqnarray}}
\newcommand{\eeqn}{\end{eqnarray}}
\newcommand{\bcross}{\phi^{\dag}}
\newcommand{\boson}{\phi^{\vphantom{\dag}}}
\newcommand{\Db}{{\cal D}\boson}
\newcommand{\Dbcross}{{\cal D}\bcross}
\newcommand{\DA}{{\cal D}A}
\newcommand{\fullint}{\int\!\!\Db\Dbcross\DA}
\newcommand{\Amu}{A_{\mu}}
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\newcommand{\WLd}[2]{\WL{#1,#2}}
\newcommand{\ep}{\epsilon}

\begin{document}




\everymath={\displaystyle}

\title{Recursive Graphical Construction for Feynman Diagrams and
Their Weights in Ginzburg-Landau Theory} 
%Application to the three-loop
%vacuum energy beta function}



\author{H. Kleinert \and A. Pelster}
\address{Institut f\"ur Theoretische Physik, Arnimallee 14 D-14195 Berlin, Germany\\
E-mails: kleinert@physik.fu-berlin.de, pelster@physik.fu-berlin.de}
\author{B. Van den Bossche}
\address{Physique Nucl\'eaire Th\'eorique, B5,
Universit\'e de Li\`ege Sart-Tilman,
 4000 Li\`ege, Belgium\\ E-mail: bvandenbossche@ulg.ac.be\\
and\\
Institut f\"ur Theoretische Physik, Arnimallee 14 D-14195 Berlin, Germany\\
E-mail: bossche@physik.fu-berlin.de}


\maketitle

\begin{abstract}
The free energy of the \gl theory satisfies a
nonlinear functional differential equation which is turned
into a recursion relation. The latter is solved graphically
order by order in the loop expansion to find all connected vacuum
diagrams, and their corresponding weights. In this way
we determine the connected vacuum diagrams and their weights up to four loops. 
\end{abstract}

\date{\today}



\section{Introduction}
\label{introduction}
Recently, two of us (H.K. and B.V.d.B.) have determined the two-loop
effective potential of $O(N)$-symmetric scalar quantum electrodynamics in $4-\ep$ dimensions
and its $\ep$-expansion \cite{kvdbeffpot}.
Going to higher loop orders requires the calculation of many complicated
Feynman integrals associated with vacuum diagrams. 
In this paper, we show how to find all these diagrams and their weights with the help of
a simple recursive technique
described in detail in Refs.~\cite{sv95,phi4,qed,bkphi4,asym}.
The basics of the method were formulated in Refs.~\cite{klrecrel,russianbook}. For simplicity, 
the present work is restricted to the theory of a single complex scalar field coupled
to electromagnetism, known as Ginzburg-Landau theory or as scalar quantum electrodynamics. 
In $D=3$ dimensions, this describes the
physics of superconductors. Without electromagnetism, we recover the physics of superfluid helium.
Here we shall restrict ourselves to the
symmetric phase, where the $O(N)$-symmetry is unbroken, which describes the system
above the critical temperature $T_c$. The more general situation will be dealt with elsewhere.

For a complex boson field, propagators are represented by
oriented lines, as in ordinary quantum electrodynamics \cite{qed}. When comparing the two expansions we must,
however, drop a minus sign for each fermion loop. In addition, the \gl theory contains four-point functions of the
scalar field which are in principle treated in $\phi^4$-theory \cite{phi4}. However,
since we deal here with complex fields, the weight of
the corresponding graphs cannot be taken from Ref.~\cite{phi4}. There is furthermore a completely
new vertex in scalar QED: the quartic seagull coupling between two photon and two
scalar fields. By a replacement of the photon lines by scalar lines, they become
equivalent to the diagrams coming from the $\phi^4$-vertex, apart, of course,
from different weights.

The paper is organized as follows. In Section~\ref{gltheory} we define more precisely the theory to be studied.
In Section~\ref{BASIC} we introduce basic functional derivatives which allow
in Section~\ref{generatingequation} to derive a functional differential equation for the free energy. From this follows
a recursion relation which allows to find all vacuum diagrams of a given order $L$ from
those of the previous orders. This equation is formulated graphically in 
Section~\ref{generatinggraphs}, where we also determine the vacuum
diagrams and the corresponding weights up to  four loops.

\section{\protect \GL theory}
\label{gltheory}
The generalized \gl theory deals with a self-interacting
complex scalar field coupled minimally to an
electromagnetic vector potential.
The theory contains two coupling constants $\g$ and $\e$. 
The field expectation value $\langle\phi\rangle$ vanishes above $T_c$
and the theory has  three types of vertices.

The physics can be extracted from the partition function
%
\be \Z=\int\Db\Dbcross\DA\exp\left( -E \right),
\label{partitionfn}
\ee
%
with thermal fluctuations being governed by the energy functional
%
\be
E(\bcross,\boson,\Amu)=\bcross_1\invG{12}\boson_2+\frac{\g}{4}
\Vg{1234}\bcross_1\boson_2\bcross_3\boson_4
+\onehalf\A{1}\invD{12}\A{2}+\e\Ve{1}{12}\A{1}\bcross_1\boson_2
+\frac{\esqr}{2} \Vesqr{12}{12}\A{1}\A{2}\bcross_1\boson_2.
\label{energy}
\ee
%
Here and below, overlined indices are used for the \elm field. We
work in a covariant gauge and assume the photon propagator to have the appropriate form (see Ref.~\cite{qed}).
Using the same notation as in Refs.~\cite{phi4,qed}, 
we keep all equations as compact as possible by assuming
Einstein's summation convention not only for the internal
degrees of freedom, but also for the space-time indices, for which repeated indices imply
an overall integral sign. In this notation the functional matrices in the energy functional (\ref{energy}) 
have the following symmetries:

\beqn
\invD{12}&=&\invD{21},\label{invDsym}\\
\Vg{1234}&=&\Vg{3214}=\Vg{1432}=\Vg{3412},\label{Vgsym}\\
\Vesqr{12}{12}&=&\Vesqr{21}{12}.\label{Vesqrsym}
\label{vertices}
\eeqn

\section{Basic Functional Derivatives}\label{BASIC}

The recursion relation will be derived by performing functional differentiations of the partition function with
respect to the propagators and their inverse as well as the vertices. 
The basic properties of these derivatives are shown in the following
equations:

\subsection*{Scalar sector}
\label{scalarsector}
\beqn
\f{\p\invG{12}}{\p\invG{34}}&=&\delta_{13}\delta_{24},\label{invGtoGfirst}\\
\f{\p\G{12}}{\p\G{34}}&=&\delta_{13}\delta_{24},\\
\f{\p\G{12}}{\p\invG{34}}&=&-\G{13}\G{42},\\
\f{\p}{\p\invG{34}}&=&-\G{13}\G{42}\f{\p}{\p\G{12}}.\label{invGtoG}
\eeqn

\subsection*{Photon sector}
\label{photonsector}
\beqn
\f{\p\invD{12}}{\p\invD{34}}&=&\onehalf\left(\deltaA{13}\deltaA{42}+
\deltaA{14}\deltaA{32}\right),\\
\f{\p\D{12}}{\p\D{34}}&=&\onehalf\left(\deltaA{13}\deltaA{42}+
\deltaA{14}\deltaA{32}\right),\\
\f{\p\D{12}}{\p\invD{34}}&=&-\onehalf\left(\D{13}\D{42}+
\D{14}\D{32}\right),\\
\f{\p}{\p\invD{34}}&=&-\D{13}\D{42}\f{\p}{\p\D{12}}.\label{invDtoD}
\eeqn

\subsection*{Vertex derivatives}

\begin{eqnarray}
\f{\p\Ve{1}{12}}{\p \Ve{2}{34}}&=&\deltaA{12}\delta_{13}\delta_{24}, \\
\frac{\delta V_{1234}}{\delta V_{5678}} &=& \frac{1}{4} \left( 
\delta_{15} \delta_{26} \delta_{37} \delta_{48} + 
\delta_{17} \delta_{26} \delta_{35} \delta_{48} + 
\delta_{15} \delta_{28} \delta_{37} \delta_{46} + 
\delta_{17} \delta_{28} \delta_{35} \delta_{46} \right),\\
\frac{\delta F_{\overline{12}12}}{\delta F_{\overline{34}34}} &=& \frac{1}{2} \left( 
\delta_{\overline{13}} \delta_{\overline{24}} \delta_{13} \delta_{24} + 
\delta_{\overline{14}} \delta_{\overline{23}} \delta_{13} \delta_{24} \right).\\ && \nonumber
\end{eqnarray}

This is a direct extension of relations used in Refs.~\cite{phi4,qed,bkphi4,asym}.
The main difference comes from the fact that the previous scalar propagators were symmetric in the indices
whereas the present propagators describing complex fields are not. By the chain rule of differentiations,
we can then find the derivative of any functional with respect to the propagators and their inverse as
well as the vertices.

\section{Functional differential equation for free energy}
\label{generatingequation}

With the definitions given in the previous section, we are now prepared to
derive the graphical recursion relation for the vacuum graphs. We start from the identity
%
\be
\fullint \f{\p}{\p\bcross_1}\left[
\bcross_2\exp\left(
-E
\right)
\right] = 0,
\label{scalarSDdef1}
\ee
%
and obtain
%
\be
\fullint\left(
\delta_{12}-\bcross_2\f{\p E}{\p\bcross_1}
\right)\exp\left(
-E
\right)= 0
\label{scalarSDdef2}
\ee
%
which, using the \gl energy functional (\ref{energy}), leads
to the linear equation
%
\be
\fullint\left(
\delta_{12}-\bcross_2\invG{13}\boson_3
- \frac{\g}{2} \Vg{1345}\bcross_2\boson_3\bcross_4\boson_5
- \frac{\esqr}{2} \Vesqr{12}{13}\A{1}\A{2}\bcross_2\boson_3
-\e\Ve{1}{13}\A{1}\bcross_2\boson_3
\right)\exp\left(-E\right)=0.
\label{scalarSDdef3}
\ee
%
Rewritten in terms of functional derivatives with respect to the inverse of the propagators,
this becomes
%
\be
\fullint\left(
\delta_{12}+\invG{13}\f{\p}{\p\invG{23}}
- \frac{\g}{2} \Vg{1345}\f{\p}{\p\invG{23}}\f{\p}{\p\invG{45}}
- \esqr \Vesqr{12}{13}\f{\p}{\p\invD{12}}\f{\p}{\p\invG{23}}
+\e\Ve{1}{13}\A{1}\f{\p}{\p\invG{23}}
\right)\exp\left(
-E
\right)=0.
\label{scalarSDdef4}
\ee
%
The last part of the above equation may be replaced by a three-vertex
derivative. However,
proceeding in this way would not lead to an iterative generation of
diagrams. For this, it is
necessary to consider a second identity:
%\footnote{The
% photon equation corresponding to~(\ref{scalarSDdef1}) does also not help in
% our quest of an iterative solution of the problem.}
%
\be
\fullint \f{\p}{\p\A{1}}\exp\left(
-E\right)= 0,
\label{photonSDdef1}
\ee
%
from which  we obtain
%
\be
\fullint
\left(
\invD{12}\A{2}+\e\Ve{1}{12}\bcross_1\boson_2
+\esqr\Vesqr{12}{12}\A{2}\bcross_1\boson_2\right)\exp\left(
-E
\right)=0,
\label{photonSDdef2}
\ee
%
or, equivalently,
%
\be
\fullint
\left(
\invD{12}\A{2}-\e\Ve{1}{12}\f{\p}{\p\invG{12}}
-\e\Vesqr{12}{12} \f{\p}{\delta \Ve{2}{12}}
\right)\exp\left(-E
\right)=0.
\label{photonSDdef3}
\ee
%
Inserting the photon-field expectation value~(\ref{photonSDdef3}) 
into~(\ref{scalarSDdef4}), we obtain
%
\beqn
&&\Bigg(
\delta_{12}+\invG{13}\f{\p}{\p\invG{23}}
-\frac{\g}{2}\Vg{1345}\f{\p}{\p\invG{23}}\f{\p}{\p\invG{45}}
-\esqr\Vesqr{12}{13}\f{\p}{\p\invD{12}}\f{\p}{\p\invG{23}}
\nonumber\\
&&\hspace{2cm}\mbox{}+
\esqr\Ve{1}{13}\D{12}\Ve{2}{45}\f{\p}{\delta \invG{23}}\f{\p}{\delta \invG{45}}
+\esqr\Ve{1}{13}\D{12}\Vesqr{23}{45}\f{\p}{\delta \invG{23}}\f{\p}{\delta \Ve{3}{45}}
\Bigg)\Z=0.
\label{Zdiffequation}
\eeqn
%
This equation is linear, but it leads to a huge number of diagrams,
both connected and disconnected.
We remove the disconnected ones by introducing 
the free energy $W$ as generating functional of the connected Green functions as
%
\be
\Z\equiv\exp\left(
\W
\right), \qquad \W=\Wfree+\Wint,
\label{Wdefinition}
\ee
%
where $\Wfree$ is the free field part
%
\be
\Wfree=-\Tr\ln\invG{}-\onehalf\Tr\ln\invDnoindex,
\ee
%
with \Tr\ being a shorthand notation
for the  functional trace. Working with the series
representation of the logarithm, we obtain directly the relations
%
\beqn
\f{\p\Wfree}{\p\invG{12}}&=&-\G{21},\label{freeinvGderiv}\\
\f{\p\Wfree}{\p\invD{12}}&=&-\onehalf\D{21},\label{freeinvDderiv} \, ,\\
\f{\p\Wfree}{\delta \Ve{1}{23}} & = & 0 \, , \label{freeinvH}
\eeqn
%
where the index ordering is important for the complex scalar
fields.

%The number of diagrams can be reduced further by dealing only with the one-particle irreducible
%diagrams. This is done with the help of a Legendre transform to determine the effective potential below $T_c$
%and will be included elsewhere. 
%We remind the reader that we have already obtained the two-loop effective
%potential of the \gl model in Ref. \cite{kvdbeffpot}.
%Using a recursion relation for the one-particle irreducible diagrams will
%allow us to generate directly all diagrams, and only these, necessary
%for calculating the effective potential to higher loop orders.

Introducing the decomposition~(\ref{Wdefinition}) in~(\ref{Zdiffequation}) and using the
relations (\ref{freeinvGderiv})--(\ref{freeinvH}),
we obtain a nonlinear functional differential equation for the interacting part $\Wint$:
%
\beqn
&&\invG{13}\f{\p\Wint}{\p\invG{23}}-\frac{\g}{2}\Vg{1345}\left[
2\G{34}\G{52}-\left(
\G{32}\f{\p\Wint}{\p\invG{45}}+\G{54}\f{\p\Wint}{\p\invG{23}}
\right)
+\f{\p^2\Wint}{\p\invG{23}\p\invG{45}}
+\f{\p\Wint}{\p\invG{23}}\f{\p\Wint}{\p\invG{45}}
\right]\nonumber\\
&&\hspace{0.5cm}\mbox{}-\esqr\Vesqr{12}{13}
\left[
\onehalf\D{21}\G{32}-\left(
\onehalf\D{21}\f{\p\Wint}{\p\invG{23}}
+\G{32}\f{\p\Wint}{\p\invD{12}}
\right)
+\f{\p^2\Wint}{\p\invD{12}\p\invG{23}}
+\f{\p\Wint}{\p\invD{12}}\f{\p\Wint}{\p\invG{23}}
\right]\nonumber\\
&&\hspace{0.5cm}\mbox{}+\esqr\Ve{1}{13}\D{12}\Ve{2}{45}
\left[
\G{52}\G{34}+\G{32}\G{54}-\left(
\G{32}\f{\p\Wint}{\p\invG{45}}+\G{54}\f{\p\Wint}{\p\invG{23}}
\right)
+\f{\p^2\Wint}{\p\invG{23}\p\invG{45}}
+\f{\p\Wint}{\p\invG{23}}\f{\p\Wint}{\p\invG{45}}
\right]\nonumber\\
&&\hspace{0.5cm}\mbox{}+\esqr\Ve{1}{13}\D{12}\Vesqr{23}{45}
\left[
-\G{32}\f{\p\Wint}{\p\Ve{3}{45}}
+\f{\p^2\Wint}{\p\invG{23}\p\Ve{3}{45}}
+\f{\p\Wint}{\p\invG{23}}\f{\p\Wint}{\p\Ve{3}{45}}
\right]=0.
\eeqn
%
With the help of Eqs.~(\ref{invGtoG}) and~(\ref{invDtoD}), 
this equation becomes
%
\beqn
&&-\G{12}\f{\p\Wint}{\p\G{12}}-\frac{\g}{2}\Vg{1234}\left[
2\G{23}\G{41}+4\G{21}\G{53}\G{46}\f{\p\Wint}{\p\G{56}}
+\G{51}\G{26}\G{73}\G{48}
\left(
\f{\p^2\Wint}{\p\G{56}\p\G{78}}
+\f{\p\Wint}{\p\G{56}}\f{\p\Wint}{\p\G{78}}
\right)
\right]\nonumber\\
&& -\esqr\Vesqr{12}{12}
\left[
\onehalf\D{21}\G{21}
+\onehalf\D{21}\G{31}\G{24}\f{\p\Wint}{\p\G{34}}
+\G{21}\D{31}\D{24}\f{\p\Wint}{\p\D{34}}
+\D{31}\D{24}\G{31}\G{24}
\left(
\f{\p^2\Wint}{\p\D{34}\p\G{34}}
+\f{\p\Wint}{\p\D{34}}\f{\p\Wint}{\p\G{34}}
\right)
\right]\nonumber\\
&&+\esqr\Ve{1}{12}\D{12}\Ve{2}{34}
\left[
\G{41}\G{23}+\G{21}\G{43}
+2\left(
\G{21}\G{53}+\G{51}\G{23}
\right)\G{46}\f{\p\Wint}{\p\G{56}}
+\G{51}\G{26}\G{73}\G{48} \left(
\f{\p^2\Wint}{\p\G{56}\p\G{78}}
\right. \right.
\nonumber\\&&
\left. \left.
+\f{\p\Wint}{\p\G{56}}\f{\p\Wint}{\p\G{78}}
\right) \right]
-\esqr\Ve{1}{12}\D{12}\Vesqr{23}{34}
\left[
\G{21}\f{\p\Wint}{\p\Ve{3}{34}}
+\G{51}\G{26}\left(
\f{\p^2\Wint}{\p\G{56}\p\Ve{3}{34}}
+\f{\p\Wint}{\p\G{56}}\f{\p\Wint}{\p\Ve{3}{34}}
\right)
\right]=0.
\label{masterequation}
\eeqn
%
From this functional differential equation, a graphical recursion relation can be derived. This is the subject
of the next section.

\section{Graphical recursion relation}
\label{generatinggraphs}


From~(\ref{masterequation}), we can derive a graphical recursion
relation for the
connected vacuum diagrams. When considering the
loop expansion of the interaction part $\Wint$, one
term is of one loop number larger than the other terms, as we now
show.

The operators $\G{12}\p/\p\G{12}$ and $\D{12}\p/\p\D{12}$ simply
count the number
of scalar lines $\quarknum$ and photon lines $\photonnum$, respectively, in a
given
diagram.
%\footnote{Since we  work with vacuum graphs, there is no need to
%introduce the number of external scalar and photon lines.}.
These numbers can be
extracted from the number and type of vertices. 
Denoting by $\Vgnum$, $\Venum$ and
$\Vesqrnum$
the number of $\g$, $\e$ and $\esqr$ vertices, we have the following 
counting rules.
The Yukawa vertex $\Ve{1}{12}$ has
one photon line and
two scalar lines, while the quartic photon-scalar vertex $\Vesqr{12}{12}$ 
has two photon lines
and two scalar
lines. Furthermore two vertex lines are necessary to produce an internal line
when combining
vertices. We have the obvious relation $2\photonnum=2\Vesqrnum+\Venum$. Taking the
quartic scalar self-interaction $V_{1234}$ into account, we have also
$2\quarknum=2\Vesqrnum+2\Venum+4\Vgnum$.
An odd number of photon fields gives no
contribution to the free energy. Thus the vertex $\e$ enters with even power.
The number of loops is then
easily found to be $\loopnum-1=\Vgnum+\Venum/2+\Vesqrnum.\label{loopnumber}$
Together, we have the counting rules
%
\beqn
\photonnum&=&\Vesqrnum+\f{\Venum}{2},\\
\quarknum&=&\Vesqrnum+\Venum+2\Vgnum,\\
\loopnum-1&=&\Vesqrnum+\f{\Venum}{2}+\Vgnum.
\eeqn
%
These relations can be inverted to give the number of each type
of vertex as a function of the number of loops, scalar, and
photon internal lines:
%
\beqn
\Vesqrnum&=&2(\loopnum-1)-\quarknum,\\
\f{\Venum}{2}&=&\quarknum+\photonnum-2(\loopnum-1),\\
\Vgnum&=&\loopnum-1-\photonnum.
\eeqn
%
It is now clear that, to count the number of scalars in a given
diagram, it is only necessary to know the loop order, as well as
the number of the quartic
$\esqr$ photon-scalar seagull vertices:
%
\be
\quarknum=2(\loopnum-1)-\Vesqrnum.
\label{Eqquarknumber}
\ee
%
The vertices $\Venum$ are not
taken into account when counting the quartic
vertices $\Vesqrnum$, which,
by definition, count the two photon-two scalar
vertices only.
The relation~(\ref{Eqquarknumber}) is interesting,
since, for complicated diagrams, with a large
loop-order, it is much less involved to count the number of quartic
$\esqr$ photon-scalar
seagull vertices than the number of scalar lines.

We are now ready to demonstrate that equation~(\ref{masterequation})
allows for a recursive solution. We form
the loop expansion
%
\be
\Wint=\sum_{\loopnum=2}^{\infty}\g^{\loopnum-1}\WL{\loopnum},
\label{Wintloop}
\ee
%
supposing that the vertices $\e$ and $\esqr$ are
of order $\sqrt{\g}$ and $\g$, respectively. This is because
the relevant parameter for the loop expansion is the  inverse
temperature $\beta=1/(k_BT)$ 
which appears as a coefficient in front of the energy. 
The inverse temperature is set equal to one in this work (see
Eq.~(\ref{partitionfn})). We could have restored it to show the
loop counting. We would have seen readily that this would have
been equivalent to the statement that
$\e$ and $\esqr$ are of order
$\sqrt{\g}$ and $\g$, respectively.
In Eq.~(\ref{Wintloop}), $\WL{\loopnum}$ is a sum over the
different diagrams of a given
order $\loopnum$:
%
\be
\WL{\loopnum}=\sum_d(-1)^{\Vgnum+\Vesqrnum}\WLd{\loopnum}{d},
\label{negativfactor} \ee
%
where $d$ distinguishes between different classes of diagrams of
the same loop order. The factor $(-1)^{\Vgnum+\Vesqrnum}$ takes care of 
minus signs in the diagrams of the perturbation expansion.
Since the number of Yukawa vertices is even, it does
not enter this prefactor: $(-1)^{\Venum}=1$. Applying the scalar
number operator on $\Wint$ gives
%
\be
\G{12}\f{\p\Wint}{\p\G{12}}=\sum_{\loopnum=2}^{\infty}\g^{\loopnum-1}
\sum_d(-1)^{\Vgnum+\Vesqrnum}\quarknum(L,d)\WLd{\loopnum}{d} \, ,
\label{countingquarklines}
\ee
%
which stresses that each class of diagrams, i.e., each topology, has
its own scalar number.

By performing the loop expansion (\ref{Wintloop}), the contributions $\WL{\loopnum}$
to the negative free energy consists of all connected vacuum diagrams constructed according to
the following Feynman rules. A straight line and a wiggly line represent the free correlation
of the scalar and the photon field, respectively:
%
\begin{fmffile}{graph09}
%
\begin{eqnarray}
%
\parbox{20mm}{\centerline{
\begin{fmfgraph*}(7,3)
\setval
\fmfleft{v1}
\fmfright{v2}
\fmf{fermion}{v2,v1}
\fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm, l.angle=-180}{v1}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}}}  
%
&\equiv &\quad G_{12}, \\
%
\parbox{20mm}{\centerline{
\begin{fmfgraph*}(7,3)
\setval
\fmfleft{v1}
\fmfright{v2}
\fmf{boson}{v1,v2}
\fmfv{decor.size=0, label=${\scs \overline{1}}$, l.dist=1mm, l.angle=-180}{v1}
\fmfv{decor.size=0, label=${\scs \overline{2}}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}}}
%
&\equiv &\quad D_{\overline{12}}.
\end{eqnarray}
%
The vertices are correspondingly pictured by
%
\begin{eqnarray}
%
\parbox{15mm}{\centerline{
\begin{fmfgraph}(5,4.33)
\setval
\fmfforce{1w,0h}{v1}
\fmfforce{0w,0h}{v2}
\fmfforce{0.5w,1h}{v3}
\fmfforce{0.5w,0.2886h}{vm}
\fmf{fermion}{v1,vm,v2}
\fmf{boson}{v3,vm}
\fmfdot{vm}
\end{fmfgraph}
}}&\equiv& \quad - e \int_{\overline{1}23} H_{\overline{1}23}\, , \label{VR1} \\
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfstraight
\fmfforce{0w,0h}{o2}
\fmfforce{0w,1h}{i1}
\fmfforce{1w,0h}{o1}
\fmfforce{1w,1h}{i2}
\fmfforce{1/2w,1/2h}{v1}
\fmf{boson}{i1,v1}
\fmf{boson}{v1,i2}
\fmf{fermion}{o1,v1}
\fmf{fermion}{v1,o2}
\fmfdot{v1}
\end{fmfgraph}
\end{center}} 
%
&\equiv& \hspace*{0.1cm} - e^2 \int_{\overline{12}34} \, F_{\overline{12}34} \, , \label{VR2}\\
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfstraight
\fmfforce{0w,0h}{o2}
\fmfforce{0w,1h}{i1}
\fmfforce{1w,0h}{o1}
\fmfforce{1w,1h}{i2}
\fmfforce{1/2w,1/2h}{v1}
\fmf{fermion}{v1,i1}
\fmf{fermion}{i2,v1}
\fmf{fermion}{v1,o1}
\fmf{fermion}{o2,v1}
\fmfdot{v1}
\end{fmfgraph}
\end{center}} 
%
&\equiv& \hspace*{0.1cm} - g \int_{1234} \, V_{1234} \, . \label{VR3}
\end{eqnarray}
%
With these Feynman rules, the insertion of the loop expansion (\ref{Wintloop}) into (\ref{masterequation}) leads to
the following equation
%
\beqn
%
&&
%
\parbox{8mm}{\begin{center}
\begin{fmfgraph*}(2.5,5)
\setval \fmfstraight \fmfforce{1w,0h}{v1} \fmfforce{1w,1h}{v2}
\fmf{fermion,left=1}{v1,v2} \fmfv{decor.size=0, label=${\scs 2}$,
l.dist=1mm, l.angle=0}{v1} \fmfv{decor.size=0, label=${\scs 1}$,
l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} g\dfermi{W^{(2)}}{1}{2} 
\hspace*{0.2cm} + \hspace*{0.1cm}
%
\parbox{8mm}{\begin{center}
\begin{fmfgraph*}(2.5,5)
\setval \fmfstraight \fmfforce{1w,0h}{v1} \fmfforce{1w,1h}{v2}
\fmf{fermion,left=1}{v1,v2} \fmfv{decor.size=0, label=${\scs 2}$,
l.dist=1mm, l.angle=0}{v1} \fmfv{decor.size=0, label=${\scs 1}$,
l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \sum_{L=3}^{\infty}g^{L-1}\dfermi{W^{(L)}}{1}{2}
%
\quad = \quad
%
% #1
%
\parbox{7mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1w,1/2h}{v2}
\fmf{fermion,right=1}{v2,v1} 
\fmf{fermion,right=1}{v1,v2} 
\fmf{photon}{v2,v1}
\fmfdot{v2,v1}
\end{fmfgraph}\end{center}}
%
% #2
%
\hspace*{1mm} + \hspace*{1mm}
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1a}
\fmfforce{1/6w,0h}{v1b}
\fmfforce{1/3w,1/2h}{v2}
\fmfforce{2/3w,1/2h}{v3}
\fmfforce{5/6w,1h}{v4a}
\fmfforce{5/6w,0h}{v4b}
\fmf{fermion,right=1}{v1a,v1b} 
\fmf{plain,right=1}{v1b,v1a} 
\fmf{plain,right=1}{v1,v2}
\fmf{photon}{v2,v3}
\fmf{fermion,right=1}{v4b,v4a} 
\fmf{plain,right=1}{v4a,v4b}
\fmfdot{v2,v3}
\end{fmfgraph}\end{center}}
%
% #3
%
\hspace*{1mm} + \frac{1}{2} \hspace*{1mm} 
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{1/4w,1h}{v1a}
\fmfforce{1/4w,0h}{v1b}
\fmfforce{1/2w,1/2h}{v2}
\fmfforce{1w,1/2h}{v3}
\fmf{fermion,right=1}{v1a,v1b} 
\fmf{plain,right=1}{v1b,v1a}
\fmf{photon,right=1}{v2,v3,v2}
\fmfdot{v2}
\end{fmfgraph}\end{center}}
%
% #4
%
\hspace*{1mm} + \hspace*{1mm}
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{1/4w,1h}{v1a}
\fmfforce{1/4w,0h}{v1b}
\fmfforce{1/2w,1/2h}{v2}
\fmfforce{3/4w,1h}{v3a}
\fmfforce{3/4w,0h}{v3b}
\fmf{fermion,right=1}{v1a,v1b} 
\fmf{plain,right=1}{v1b,v1a}
\fmf{plain,right=1}{v3a,v3b}
\fmf{fermion,right=1}{v3b,v3a}
\fmfdot{v2}
\end{fmfgraph}\end{center}}
\quad + \quad
%
%
\no\\ &&
%
\quad\sum_{L=2}^{\infty}g^{L-1}\Biggl[
%
% #1
%
2 \hspace*{0.2cm}
%
\parbox{12mm}{\begin{center}
\begin{fmfgraph*}(10,8)
\setval \fmfstraight \fmfforce{2.5/9w,1.5/8h}{v1}
\fmfforce{2.5/9w,6.5/8h}{v2} \fmfforce{5/9w,1/2h}{v3}
\fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion,left=1}{v1,v2} \fmf{plain,left=1}{v2,v1}
\fmf{fermion}{v3,v5} \fmf{fermion}{v4,v3} \fmfdot{v3}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \dfermi{W^{(L)}}{1}{2}
%
% #2
%
\hspace*{0.2cm} + \hspace*{0.1cm} \frac{1}{2} \hspace*{0.2cm}
%
\parbox{8mm}{\begin{center}
\begin{fmfgraph*}(5,10)
\setval \fmfstraight \fmfforce{0w,1/2h}{v1} \fmfforce{1w,0h}{v2}
\fmfforce{1w,1/3h}{v3} \fmfforce{1w,2/3h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion}{v2,v1} \fmf{fermion}{v1,v3} \fmf{fermion}{v4,v1}
\fmf{fermion}{v1,v5} \fmfdot{v1} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=0}{v5} \fmfv{decor.size=0, label=${\scs
2}$, l.dist=1mm, l.angle=0}{v4} \fmfv{decor.size=0, label=${\scs
3}$, l.dist=1mm, l.angle=0}{v3} \fmfv{decor.size=0, label=${\scs
4}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \ddfermi{W^{(L)}}
%
% #3
%
\hspace*{0.2cm} + \hspace*{0.1cm} \frac{1}{2} \hspace*{0.2cm}
%
\parbox{12mm}{\begin{center}
\begin{fmfgraph*}(10,8)
\setval \fmfstraight \fmfforce{2.5/9w,1.5/8h}{v1}
\fmfforce{2.5/9w,6.5/8h}{v2} \fmfforce{5/9w,1/2h}{v3}
\fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{boson,left=1}{v1,v2,v1} \fmf{fermion}{v3,v5}
\fmf{fermion}{v4,v3} \fmfdot{v3} \fmfv{decor.size=0, label=${\scs
2}$, l.dist=1mm, l.angle=0}{v4} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \dfermi{W^{(L)}}{1}{2}
%
\no \\ && \hspace*{1cm}
%
% #4
%
+ \hspace*{0.2cm} 
%
\parbox{12mm}{\begin{center}
\begin{fmfgraph*}(9,8)
\setval \fmfstraight \fmfforce{2.5/9w,1.5/8h}{v1}
\fmfforce{2.5/9w,6.5/8h}{v2} \fmfforce{5/9w,1/2h}{v3}
\fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion,left=1}{v1,v2} \fmf{plain,left=1}{v2,v1}
\fmf{boson}{v3,v5} \fmf{boson}{v4,v3} \fmfdot{v3}
\fmfv{decor.size=0, label=${\scs \bar{2}}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs \bar{1}}$, l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \dbphi{W^{(L)}}{$\bar{1}$}{$\bar{2}$}
%
% #5
%
\hspace*{0.2cm} + \hspace*{0.2cm}
%
\parbox{12mm}{\begin{center}
\begin{fmfgraph*}(5,10)
\setval \fmfstraight \fmfforce{0w,1/2h}{v1} \fmfforce{1w,0h}{v2}
\fmfforce{1w,1/3h}{v3} \fmfforce{1w,2/3h}{v4} \fmfforce{1w,1h}{v5}
\fmf{boson}{v2,v1} \fmf{boson}{v1,v3} \fmf{fermion}{v4,v1}
\fmf{fermion}{v1,v5} \fmfdot{v1} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=0}{v5} \fmfv{decor.size=0, label=${\scs
2}$, l.dist=1mm, l.angle=0}{v4} \fmfv{decor.size=0, label=${\scs
\bar{1}}$, l.dist=1mm, l.angle=0}{v3} \fmfv{decor.size=0, label=${\scs
\bar{2}}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \ddbfermi{W^{(L)}}
%
% #6
%
\hspace*{0.2cm} + \hspace*{0.1cm} 2 \hspace*{0.2cm}
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph*}(14,8)
\setval \fmfstraight \fmfforce{2.5/14w,1.5/8h}{v1}
\fmfforce{2.5/14w,6.5/8h}{v2} \fmfforce{5/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4} \fmfforce{1w,0h}{v5}
\fmfforce{1w,1h}{v6} \fmf{fermion,right=1}{v2,v1}
\fmf{plain,left=1}{v2,v1} \fmf{boson}{v3,v4} \fmf{fermion}{v5,v4}
\fmf{fermion}{v4,v6} \fmfdot{v3,v4} \fmfv{decor.size=0,
label=${\scs 1}$, l.dist=1mm, l.angle=0}{v6} \fmfv{decor.size=0,
label=${\scs 2}$, l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \dfermi{W^{(L)}}{1}{2}
%
% #7
%
\hspace*{0.2cm} + \hspace*{0.1cm} 2 \hspace*{0.2cm}
%
\parbox{10.5mm}{\begin{center}
\begin{fmfgraph*}(7.5,5)
\setval \fmfstraight \fmfforce{1/3w,0h}{v1} \fmfforce{1/3w,1h}{v2}
\fmfforce{1w,0h}{v3} \fmfforce{1w,1h}{v4}
\fmf{fermion,left=1}{v1,v2} \fmf{fermion}{v2,v4}
\fmf{fermion}{v3,v1} \fmf{boson}{v1,v2} \fmfdot{v1,v2}
\fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm, l.angle=0}{v3}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \dfermi{W^{(L)}}{1}{2}
%
\no \\ && \hspace*{1cm}
%
% #8
%
+ \hspace*{0.2cm}
%
\parbox{8mm}{\begin{center}
\begin{fmfgraph*}(5,10)
\setval \fmfstraight \fmfforce{0w,1/6h}{v1a}
\fmfforce{0w,5/6h}{v1b} \fmfforce{1w,0h}{v2}
\fmfforce{1w,1/3h}{v3} \fmfforce{1w,2/3h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion}{v2,v1a} \fmf{fermion}{v1a,v3} \fmf{fermion}{v4,v1b}
\fmf{fermion}{v1b,v5} \fmf{boson}{v1a,v1b} \fmfdot{v1a,v1b}
\fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm, l.angle=0}{v5}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs 3}$, l.dist=1mm, l.angle=0}{v3}
\fmfv{decor.size=0, label=${\scs 4}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \ddfermi{W^{(L)}}
%
% #9
%
\hspace*{0.2cm} + \hspace*{0.2cm}
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph*}(14,8)
\setval \fmfstraight \fmfforce{2.5/14w,1.5/8h}{v1}
\fmfforce{2.5/14w,6.5/8h}{v2} \fmfforce{5/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4} \fmfforce{1w,0h}{v5}
\fmfforce{1w,1h}{v6} \fmfforce{1w,1/2h}{v7}
\fmf{fermion,right=1}{v2,v1} \fmf{plain,right=1}{v1,v2}
\fmf{boson}{v4,v3} \fmf{fermion}{v5,v4} \fmf{fermion}{v4,v7}
\fmf{boson}{v4,v6} \fmfdot{v3,v4} \fmfv{decor.size=0,
label=${\scs \bar{1}}$, l.dist=1mm, l.angle=0}{v6} \fmfv{decor.size=0,
label=${\scs 2}$, l.dist=1mm, l.angle=0}{v5} \fmfv{decor.size=0,
label=${\scs 1}$, l.dist=1mm, l.angle=0}{v7}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dvertex{W^{(L)}}{$\bar{1}$}{2}{1}
%
% #10
%
\hspace*{0.2cm} + \hspace*{0.2cm}
%
\parbox{8mm}{\begin{center}
\begin{fmfgraph*}(5,13)
\setval \fmfstraight \fmfforce{0w,7/8h}{v1a}
\fmfforce{0w,1/4h}{v1b} \fmfforce{1w,0h}{v2}
\fmfforce{1w,1/4h}{v3} \fmfforce{1w,2/4h}{v4}
\fmfforce{1w,3/4h}{v5} \fmfforce{1w,1h}{v6} \fmf{fermion}{v2,v1b}
\fmf{fermion}{v1b,v3} \fmf{boson}{v4,v1b} \fmf{fermion}{v5,v1a}
\fmf{fermion}{v1a,v6} \fmf{boson}{v1a,v1b} \fmfdot{v1a,v1b}
\fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm, l.angle=0}{v6}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm, l.angle=0}{v5}
\fmfv{decor.size=0, label=${\scs \bar{1}}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs 3}$, l.dist=1mm, l.angle=0}{v3}
\fmfv{decor.size=0, label=${\scs 4}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \ddvertex{W^{(L)}}{1}{2}{$\bar{1}$}{3}{4}
%\Biggr]
\no \\
&& \hspace*{1cm}
%
% #11
%
%\sum_{L=3}^{\infty}\Biggl[
+ \hspace*{0.1cm} \frac{1}{2}
\hspace*{0.1cm} \sum_{L'=2}^{L-1}
\hspace*{0.1cm}\dfermi{W^{(L')}}{1}{2} \hspace*{0.3cm}
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph*}(8,8)
\setval \fmfstraight \fmfforce{0w,0h}{v1} \fmfforce{0w,1h}{v2}
\fmfforce{1/2w,1/2h}{v3} \fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion}{v1,v3} \fmf{fermion}{v3,v2} \fmf{fermion}{v4,v3}
\fmf{fermion}{v3,v5} \fmfdot{v3} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=-180}{v2} \fmfv{decor.size=0,
label=${\scs 2}$, l.dist=1mm, l.angle=-180}{v1}
\fmfv{decor.size=0, label=${\scs 3}$, l.dist=1mm, l.angle=0}{v5}
\fmfv{decor.size=0, label=${\scs 4}$, l.dist=1mm, l.angle=0}{v4}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dfermi{W^{(L-L'+1)}}{3}{4}
%
% #12
%
\hspace*{0.2cm} + \hspace*{0.2cm}
\sum_{L'=2}^{L-1} \hspace*{0.1cm}\dfermi{W^{(L')}}{1}{2}
\hspace*{0.3cm}
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph*}(8,8)
\setval \fmfstraight \fmfforce{0w,0h}{v1} \fmfforce{0w,1h}{v2}
\fmfforce{1/2w,1/2h}{v3} \fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion}{v1,v3} \fmf{fermion}{v3,v2} \fmf{boson}{v4,v3}
\fmf{boson}{v3,v5} \fmfdot{v3} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=-180}{v2} \fmfv{decor.size=0,
label=${\scs 2}$, l.dist=1mm, l.angle=-180}{v1}
\fmfv{decor.size=0, label=${\scs \bar{1}}$, l.dist=1mm, l.angle=0}{v5}
\fmfv{decor.size=0, label=${\scs \bar{2}}$, l.dist=1mm, l.angle=0}{v4}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dbphi{W^{(L-L'+1)}}{$\bar{1}$}{$\bar{2}$}
%
\no \\ && \hspace*{1cm}
%
% #13
%
+  \hspace*{0.2cm} \sum_{L'=2}^{L-1}
\hspace*{0.1cm}\dfermi{W^{(L')}}{1}{2} \hspace*{0.3cm}
%
\parbox{16mm}{\begin{center}
\begin{fmfgraph*}(13,8)
\setval \fmfstraight \fmfforce{0w,0h}{v1} \fmfforce{0w,1h}{v2}
\fmfforce{4/13w,1/2h}{v3} \fmfforce{9/13w,1/2h}{v4}
\fmfforce{1w,0h}{v5} \fmfforce{1w,1h}{v6} \fmf{fermion}{v1,v3}
\fmf{fermion}{v3,v2} \fmf{boson}{v4,v3} \fmf{fermion}{v5,v4}
\fmf{fermion}{v4,v6} \fmfdot{v3,v4} \fmfv{decor.size=0,
label=${\scs 1}$, l.dist=1mm, l.angle=-180}{v2}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm,
l.angle=-180}{v1} \fmfv{decor.size=0, label=${\scs 3}$,
l.dist=1mm, l.angle=0}{v6} \fmfv{decor.size=0, label=${\scs 4}$,
l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dfermi{W^{(L-L'+1)}}{3}{4}
%
% #14
%
\hspace*{0.2cm} + \hspace*{0.2cm}
\sum_{L'=2}^{L-1} \hspace*{0.1cm}\dfermi{W^{(L')}}{1}{2}
\hspace*{0.3cm}
%
\parbox{16mm}{\begin{center}
\begin{fmfgraph*}(13,8)
\setval \fmfstraight \fmfforce{0w,0h}{v1} \fmfforce{0w,1h}{v2}
\fmfforce{4/13w,1/2h}{v3} \fmfforce{9/13w,1/2h}{v4}
\fmfforce{1w,0h}{v5} \fmfforce{1w,1h}{v6} \fmfforce{1w,1/2h}{v7}
\fmf{fermion}{v1,v3} \fmf{fermion}{v3,v2} \fmf{boson}{v4,v3}
\fmf{fermion}{v5,v4} \fmf{fermion}{v4,v7} \fmf{boson}{v4,v6}
\fmfdot{v3,v4} \fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm,
l.angle=-180}{v2} \fmfv{decor.size=0, label=${\scs 2}$,
l.dist=1mm, l.angle=-180}{v1} \fmfv{decor.size=0, label=${\scs
\bar{1}}$, l.dist=1mm, l.angle=0}{v6} \fmfv{decor.size=0, label=${\scs
4}$, l.dist=1mm, l.angle=0}{v5} \fmfv{decor.size=0, label=${\scs
3}$, l.dist=1mm, l.angle=0}{v7}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dvertex{W^{(L-L'+1)}}{$\bar{1}$}{4}{3} \Biggr],
%
\label{grapheq2}
\eeqn
%
\end{fmffile}
%
which we have written directly as a graphical equation where the
vertices already contain the coupling constants $\e,\esqr,g$. 
The last
four terms are the nonlinear ones. They start to give a
contribution only at the three-loop level. (Although the  overall
summation starts at $L'=2$, the nonlinear terms have an internal
summation for $L'\in [2,L-1]$, leading to a vanishing two-loop
contribution.) The fact that only positive signs enter is a
consequence of the Feynman rules (\ref{VR1})--(\ref{VR2}).

The term $\WL{2}$, corresponding to two-loop diagrams, is the
initial condition to enter this equation. It needs not to be given
because it is  also contained in~(\ref{grapheq2}). Identifying the 
terms of order $g$, we see directly that only the first line survives.
Integrating the equation gives the four diagrams in the right-hand-side, with
the corresponding weights $1/2,1/2,1/2,1/2$ obtained by dividing each
graph by its number of scalar lines (compare Table I):
%
\begin{fmffile}{graph10}
%
\begin{eqnarray}
W^{(2)} = 
%
% #1
%
\frac{1}{2}
%
\parbox{7mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1w,1/2h}{v2}
\fmf{fermion,right=1}{v2,v1} 
\fmf{fermion,right=1}{v1,v2} 
\fmf{photon}{v2,v1}
\fmfdot{v2,v1}
\end{fmfgraph}\end{center}}
%
\hspace*{0.2cm} + \hspace*{0.2cm}
%
% #2
%
\frac{1}{2}
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1a}
\fmfforce{1/6w,0h}{v1b}
\fmfforce{1/3w,1/2h}{v2}
\fmfforce{2/3w,1/2h}{v3}
\fmfforce{5/6w,1h}{v4a}
\fmfforce{5/6w,0h}{v4b}
\fmf{fermion,right=1}{v1a,v1b} 
\fmf{plain,right=1}{v1b,v1a} 
\fmf{plain,right=1}{v1,v2}
\fmf{photon}{v2,v3}
\fmf{fermion,right=1}{v4b,v4a} 
\fmf{plain,right=1}{v4a,v4b}
\fmfdot{v2,v3}
\end{fmfgraph}\end{center}}
%
\hspace*{0.2cm} + \hspace*{0.2cm}
%
% #3
%
\frac{1}{2}\,
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{1/4w,1h}{v1a}
\fmfforce{1/4w,0h}{v1b}
\fmfforce{1/2w,1/2h}{v2}
\fmfforce{1w,1/2h}{v3}
\fmf{fermion,right=1}{v1a,v1b} 
\fmf{plain,right=1}{v1b,v1a}
\fmf{photon,right=1}{v2,v3,v2}
\fmfdot{v2}
\end{fmfgraph}\end{center}}
%
\hspace*{0.2cm} + \hspace*{0.2cm}
%
% #4
%
\frac{1}{2}\,
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{1/4w,1h}{v1a}
\fmfforce{1/4w,0h}{v1b}
\fmfforce{1/2w,1/2h}{v2}
\fmfforce{3/4w,1h}{v3a}
\fmfforce{3/4w,0h}{v3b}
\fmf{fermion,right=1}{v1a,v1b} 
\fmf{plain,right=1}{v1b,v1a}
\fmf{plain,right=1}{v3a,v3b}
\fmf{fermion,right=1}{v3b,v3a}
\fmfdot{v2}
\end{fmfgraph}\end{center}}
%
\end{eqnarray}
%
Equating powers of  $\g$, we
end up with the following nonlinear graphical recursion relation
for the vacuum diagrams:
%
%
\beqn
%
&&
%
\parbox{8mm}{\begin{center}
\begin{fmfgraph*}(2.5,5)
\setval \fmfstraight \fmfforce{1w,0h}{v1} \fmfforce{1w,1h}{v2}
\fmf{fermion,left=1}{v1,v2} \fmfv{decor.size=0, label=${\scs 2}$,
l.dist=1mm, l.angle=0}{v1} \fmfv{decor.size=0, label=${\scs 1}$,
l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \dfermi{W^{(L+1)}}{1}{2} \quad = \quad
%
% #1
%
2 \hspace*{0.2cm}
%
\parbox{12mm}{\begin{center}
\begin{fmfgraph*}(10,8)
\setval \fmfstraight \fmfforce{2.5/9w,1.5/8h}{v1}
\fmfforce{2.5/9w,6.5/8h}{v2} \fmfforce{5/9w,1/2h}{v3}
\fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion,left=1}{v1,v2} \fmf{plain,left=1}{v2,v1}
\fmf{fermion}{v3,v5} \fmf{fermion}{v4,v3} \fmfdot{v3}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \dfermi{W^{(L)}}{1}{2}
%
% #2
%
\hspace*{0.2cm} + \hspace*{0.1cm} \frac{1}{2} \hspace*{0.2cm}
%
\parbox{8mm}{\begin{center}
\begin{fmfgraph*}(5,10)
\setval \fmfstraight \fmfforce{0w,1/2h}{v1} \fmfforce{1w,0h}{v2}
\fmfforce{1w,1/3h}{v3} \fmfforce{1w,2/3h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion}{v2,v1} \fmf{fermion}{v1,v3} \fmf{fermion}{v4,v1}
\fmf{fermion}{v1,v5} \fmfdot{v1} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=0}{v5} \fmfv{decor.size=0, label=${\scs
2}$, l.dist=1mm, l.angle=0}{v4} \fmfv{decor.size=0, label=${\scs
3}$, l.dist=1mm, l.angle=0}{v3} \fmfv{decor.size=0, label=${\scs
4}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \ddfermi{W^{(L)}}
%
% #3
%
\hspace*{0.2cm} + \hspace*{0.1cm} \frac{1}{2} \hspace*{0.2cm}
%
\parbox{12mm}{\begin{center}
\begin{fmfgraph*}(10,8)
\setval \fmfstraight \fmfforce{2.5/9w,1.5/8h}{v1}
\fmfforce{2.5/9w,6.5/8h}{v2} \fmfforce{5/9w,1/2h}{v3}
\fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{boson,left=1}{v1,v2,v1} \fmf{fermion}{v3,v5}
\fmf{fermion}{v4,v3} \fmfdot{v3} \fmfv{decor.size=0, label=${\scs
2}$, l.dist=1mm, l.angle=0}{v4} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \dfermi{W^{(L)}}{1}{2}
%
\no \\ && \hspace*{1cm}
%
% #4
%
+ \hspace*{0.2cm}
%
\parbox{12mm}{\begin{center}
\begin{fmfgraph*}(9,8)
\setval \fmfstraight \fmfforce{2.5/9w,1.5/8h}{v1}
\fmfforce{2.5/9w,6.5/8h}{v2} \fmfforce{5/9w,1/2h}{v3}
\fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion,left=1}{v1,v2} \fmf{plain,left=1}{v2,v1}
\fmf{boson}{v3,v5} \fmf{boson}{v4,v3} \fmfdot{v3}
\fmfv{decor.size=0, label=${\scs \bar{2}}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs \bar{1}}$, l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \dbphi{W^{(L)}}{$\bar{1}$}{$\bar{2}$}
%
% #5
%
\hspace*{0.2cm} + \hspace*{0.2cm}
%
\parbox{12mm}{\begin{center}
\begin{fmfgraph*}(5,10)
\setval \fmfstraight \fmfforce{0w,1/2h}{v1} \fmfforce{1w,0h}{v2}
\fmfforce{1w,1/3h}{v3} \fmfforce{1w,2/3h}{v4} \fmfforce{1w,1h}{v5}
\fmf{boson}{v2,v1} \fmf{boson}{v1,v3} \fmf{fermion}{v4,v1}
\fmf{fermion}{v1,v5} \fmfdot{v1} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=0}{v5} \fmfv{decor.size=0, label=${\scs
2}$, l.dist=1mm, l.angle=0}{v4} \fmfv{decor.size=0, label=${\scs
\bar{1}}$, l.dist=1mm, l.angle=0}{v3} \fmfv{decor.size=0, label=${\scs
\bar{2}}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \ddbfermi{W^{(L)}}
%
% #6
%
\hspace*{0.2cm} + \hspace*{0.1cm} 2 \hspace*{0.2cm}
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph*}(14,8)
\setval \fmfstraight \fmfforce{2.5/14w,1.5/8h}{v1}
\fmfforce{2.5/14w,6.5/8h}{v2} \fmfforce{5/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4} \fmfforce{1w,0h}{v5}
\fmfforce{1w,1h}{v6} \fmf{fermion,right=1}{v2,v1}
\fmf{plain,left=1}{v2,v1} \fmf{boson}{v3,v4} \fmf{fermion}{v5,v4}
\fmf{fermion}{v4,v6} \fmfdot{v3,v4} \fmfv{decor.size=0,
label=${\scs 1}$, l.dist=1mm, l.angle=0}{v6} \fmfv{decor.size=0,
label=${\scs 2}$, l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \dfermi{W^{(L)}}{1}{2}
%
% #7
%
\hspace*{0.2cm} + \hspace*{0.1cm} 2 \hspace*{0.2cm}
%
\parbox{10.5mm}{\begin{center}
\begin{fmfgraph*}(7.5,5)
\setval \fmfstraight \fmfforce{1/3w,0h}{v1} \fmfforce{1/3w,1h}{v2}
\fmfforce{1w,0h}{v3} \fmfforce{1w,1h}{v4}
\fmf{fermion,left=1}{v1,v2} \fmf{fermion}{v2,v4}
\fmf{fermion}{v3,v1} \fmf{boson}{v1,v2} \fmfdot{v1,v2}
\fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm, l.angle=0}{v3}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \dfermi{W^{(L)}}{1}{2}
%
\no \\ && \hspace*{1cm}
%
% #8
%
+ \hspace*{0.2cm}
%
\parbox{8mm}{\begin{center}
\begin{fmfgraph*}(5,10)
\setval \fmfstraight \fmfforce{0w,1/6h}{v1a}
\fmfforce{0w,5/6h}{v1b} \fmfforce{1w,0h}{v2}
\fmfforce{1w,1/3h}{v3} \fmfforce{1w,2/3h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion}{v2,v1a} \fmf{fermion}{v1a,v3} \fmf{fermion}{v4,v1b}
\fmf{fermion}{v1b,v5} \fmf{boson}{v1a,v1b} \fmfdot{v1a,v1b}
\fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm, l.angle=0}{v5}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs 3}$, l.dist=1mm, l.angle=0}{v3}
\fmfv{decor.size=0, label=${\scs 4}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.2cm} \ddfermi{W^{(L)}}
%
% #9
%
\hspace*{0.2cm} + \hspace*{0.2cm}
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph*}(14,8)
\setval \fmfstraight \fmfforce{2.5/14w,1.5/8h}{v1}
\fmfforce{2.5/14w,6.5/8h}{v2} \fmfforce{5/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4} \fmfforce{1w,0h}{v5}
\fmfforce{1w,1h}{v6} \fmfforce{1w,1/2h}{v7}
\fmf{fermion,right=1}{v2,v1} \fmf{plain,right=1}{v1,v2}
\fmf{boson}{v4,v3} \fmf{fermion}{v5,v4} \fmf{fermion}{v4,v7}
\fmf{boson}{v4,v6} \fmfdot{v3,v4} \fmfv{decor.size=0,
label=${\scs \bar{1}}$, l.dist=1mm, l.angle=0}{v6} \fmfv{decor.size=0,
label=${\scs 2}$, l.dist=1mm, l.angle=0}{v5} \fmfv{decor.size=0,
label=${\scs 1}$, l.dist=1mm, l.angle=0}{v7}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dvertex{W^{(L)}}{$\bar{1}$}{2}{1}
%
% #10
%
\hspace*{0.2cm} + \hspace*{0.2cm}
%
\parbox{8mm}{\begin{center}
\begin{fmfgraph*}(5,13)
\setval \fmfstraight \fmfforce{0w,7/8h}{v1a}
\fmfforce{0w,1/4h}{v1b} \fmfforce{1w,0h}{v2}
\fmfforce{1w,1/4h}{v3} \fmfforce{1w,2/4h}{v4}
\fmfforce{1w,3/4h}{v5} \fmfforce{1w,1h}{v6} \fmf{fermion}{v2,v1b}
\fmf{fermion}{v1b,v3} \fmf{boson}{v4,v1b} \fmf{fermion}{v5,v1a}
\fmf{fermion}{v1a,v6} \fmf{boson}{v1a,v1b} \fmfdot{v1a,v1b}
\fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm, l.angle=0}{v6}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm, l.angle=0}{v5}
\fmfv{decor.size=0, label=${\scs \bar{1}}$, l.dist=1mm, l.angle=0}{v4}
\fmfv{decor.size=0, label=${\scs 3}$, l.dist=1mm, l.angle=0}{v3}
\fmfv{decor.size=0, label=${\scs 4}$, l.dist=1mm, l.angle=0}{v2}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm} \ddvertex{W^{(L)}}{1}{2}{$\bar{1}$}{3}{4} \no \\ &&
\hspace*{1cm}
%
% #11
%
+ \hspace*{0.1cm} \frac{1}{2} \hspace*{0.1cm} \sum_{L'=2}^{L-1}
\hspace*{0.1cm}\dfermi{W^{(L')}}{1}{2} \hspace*{0.3cm}
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph*}(8,8)
\setval \fmfstraight \fmfforce{0w,0h}{v1} \fmfforce{0w,1h}{v2}
\fmfforce{1/2w,1/2h}{v3} \fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion}{v1,v3} \fmf{fermion}{v3,v2} \fmf{fermion}{v4,v3}
\fmf{fermion}{v3,v5} \fmfdot{v3} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=-180}{v2} \fmfv{decor.size=0,
label=${\scs 2}$, l.dist=1mm, l.angle=-180}{v1}
\fmfv{decor.size=0, label=${\scs 3}$, l.dist=1mm, l.angle=0}{v5}
\fmfv{decor.size=0, label=${\scs 4}$, l.dist=1mm, l.angle=0}{v4}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dfermi{W^{(L-L'+1)}}{3}{4}
%
% #12
%
\hspace*{0.2cm} + \hspace*{0.2cm}
\sum_{L'=2}^{L-1} \hspace*{0.1cm}\dfermi{W^{(L')}}{1}{2}
\hspace*{0.3cm}
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph*}(8,8)
\setval \fmfstraight \fmfforce{0w,0h}{v1} \fmfforce{0w,1h}{v2}
\fmfforce{1/2w,1/2h}{v3} \fmfforce{1w,0h}{v4} \fmfforce{1w,1h}{v5}
\fmf{fermion}{v1,v3} \fmf{fermion}{v3,v2} \fmf{boson}{v4,v3}
\fmf{boson}{v3,v5} \fmfdot{v3} \fmfv{decor.size=0, label=${\scs
1}$, l.dist=1mm, l.angle=-180}{v2} \fmfv{decor.size=0,
label=${\scs 2}$, l.dist=1mm, l.angle=-180}{v1}
\fmfv{decor.size=0, label=${\scs \bar{1}}$, l.dist=1mm, l.angle=0}{v5}
\fmfv{decor.size=0, label=${\scs \bar{2}}$, l.dist=1mm, l.angle=0}{v4}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dbphi{W^{(L-L'+1)}}{$\bar{1}$}{$\bar{2}$}
%
\no \\ && \hspace*{1cm}
%
% #13
%
+ \hspace*{0.2cm}  \sum_{L'=2}^{L-1}
\hspace*{0.1cm}\dfermi{W^{(L')}}{1}{2} \hspace*{0.3cm}
%
\parbox{16mm}{\begin{center}
\begin{fmfgraph*}(13,8)
\setval \fmfstraight \fmfforce{0w,0h}{v1} \fmfforce{0w,1h}{v2}
\fmfforce{4/13w,1/2h}{v3} \fmfforce{9/13w,1/2h}{v4}
\fmfforce{1w,0h}{v5} \fmfforce{1w,1h}{v6} \fmf{fermion}{v1,v3}
\fmf{fermion}{v3,v2} \fmf{boson}{v4,v3} \fmf{fermion}{v5,v4}
\fmf{fermion}{v4,v6} \fmfdot{v3,v4} \fmfv{decor.size=0,
label=${\scs 1}$, l.dist=1mm, l.angle=-180}{v2}
\fmfv{decor.size=0, label=${\scs 2}$, l.dist=1mm,
l.angle=-180}{v1} \fmfv{decor.size=0, label=${\scs 3}$,
l.dist=1mm, l.angle=0}{v6} \fmfv{decor.size=0, label=${\scs 4}$,
l.dist=1mm, l.angle=0}{v5}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dfermi{W^{(L-L'+1)}}{3}{4}
%
% #14
%
\hspace*{0.2cm} + \hspace*{0.2cm}
\sum_{L'=2}^{L-1} \hspace*{0.1cm}\dfermi{W^{(L')}}{1}{2}
\hspace*{0.3cm}
%
\parbox{16mm}{\begin{center}
\begin{fmfgraph*}(13,8)
\setval \fmfstraight \fmfforce{0w,0h}{v1} \fmfforce{0w,1h}{v2}
\fmfforce{4/13w,1/2h}{v3} \fmfforce{9/13w,1/2h}{v4}
\fmfforce{1w,0h}{v5} \fmfforce{1w,1h}{v6} \fmfforce{1w,1/2h}{v7}
\fmf{fermion}{v1,v3} \fmf{fermion}{v3,v2} \fmf{boson}{v4,v3}
\fmf{fermion}{v5,v4} \fmf{fermion}{v4,v7} \fmf{boson}{v4,v6}
\fmfdot{v3,v4} \fmfv{decor.size=0, label=${\scs 1}$, l.dist=1mm,
l.angle=-180}{v2} \fmfv{decor.size=0, label=${\scs 2}$,
l.dist=1mm, l.angle=-180}{v1} \fmfv{decor.size=0, label=${\scs
\bar{1}}$, l.dist=1mm, l.angle=0}{v6} \fmfv{decor.size=0, label=${\scs
4}$, l.dist=1mm, l.angle=0}{v5} \fmfv{decor.size=0, label=${\scs
3}$, l.dist=1mm, l.angle=0}{v7}
\end{fmfgraph*}
\end{center}}
%
\hspace*{0.3cm}\dvertex{W^{(L-L'+1)}}{$\bar{1}$}{4}{3}.
%
\label{grapheq5}
\eeqn
%
\end{fmffile}
%

The recursive nature of this equation is due to the fact that the
left-hand-side  is of one higher loop order than the right-hand-side:
To obtain the diagrams at order $L+1$, one applies the  right-hand-side 
operators on the
lower order diagrams. Since the left-hand-side contains the 
scalar number operator 
for each diagram, the weight of the diagram which have just been
obtained has to be divided by the respective number of scalar lines, see
Eq.~(\ref{countingquarklines}). We remind the reader that this 
number can be obtained knowing
the number of seagull vertices of the respective diagram, see Eq.~(\ref{Eqquarknumber}).

We have derived the vacuum diagrams of the \gl
theory up to four loops which involves the nonlinear
part of Eq.~(\ref{grapheq5}). Indeed, the nonlinear terms only
enter from the three-loop order. The resulting
diagrams are given in Table~1. The effort needed to obtain them is
considerably reduced compared to a calculation done with the help of external sources coupled linearily to the fields.
Note that Eq.~(\ref{grapheq5}) is
suitable for an automatized symbolic computation which can be implemented as in Ref. \cite{phi4}, 
such that one may proceed to higher orders without much
effort except for computer time. 

A look at Table 1 shows that the diagrams and weights
of the Yukawa part coincide with those from Ref.~\cite{qed}, as it
should. For the pure $\phi^4$-part, the diagrams are equivalent
to those in Ref.~\cite{phi4}, although the weights do not
coincide, since we deal with complex scalar fields.

Being in the possession of all Feynman diagrams we must still
calculate the associated integrals in order to extract physical results.
This will be done in a separate publication. In particular, we intend to compute the vacuum energy which
determines the critical behavior of the heat capacity of a superconductor at the phase transition.

\section{Conclusions}
\label{conclusions}

In this paper, we set up a graphical recursion relation for obtaining the
connected diagrams of the \gl model which describes superconductors near the critical point. We have used our
equation to obtain the diagrams up to the four-loop order.
These diagrams will be needed to extend our two-loop calculations in
Ref.~\cite{kvdbeffpot} to higher orders.

\section*{Acknowledgement}

The work of B.V.d.B. was supported by the Alexander von Humboldt foundation and the Institut Interuniversitaire
des Sciences Nucl\'eaires de Belgique.

\begin{thebibliography}{99}
%
\bibitem{kvdbeffpot}
H. Kleinert and B. Van den Bossche,
{\em Two-loop effective potential of $O(N)$-symmetric scalar QED in $4-\ep$
dimensions}; eprint: cond-mat/0104102.
%
\bibitem{sv95}
S. Schelstraete and H. Verschelde,
Z. Phys. C {\bf 67}, 347 (1995).
%
\bibitem{phi4}
H. Kleinert, A. Pelster, B. Kastening, and M. Bachmann,
Phys. Rev. E {\bf 62}, 1537 (2000); eprint: hep-th/9907168.
%
\bibitem{qed}
M. Bachmann, H. Kleinert, and A. Pelster,
Phys. Rev. D {\bf 61}, 085017 (2000); eprint: hep-th/9907044.
%
\bibitem{bkphi4}
B. Kastening, Phys. Rev. E {\bf 61}, 3501 (2000); eprint: hep-th/9908172.
%
\bibitem{asym}
H. Kleinert and A. Pelster, {\em Functional differential equations for the 
free energy and the effective energy in the broken-symmetry phase of
$\phi^4$-theory and their recursive graphical solution}; eprint: hep-th/0006153. 
%
\bibitem{klrecrel}
H. Kleinert, Fortschr. Phys. {\bf 30}, 187 (1982);
H. Kleinert, Fortschr. Phys. {\bf 30}, 351 (1982).
%
\bibitem{russianbook}
A.N. Vasiliev, {\em Functional Methods in Quantum Field Theory and Statistical Physics}
(Gordon and Breach Science Publishers, New York, 1998); translation from the Russian edition
(St. Petersburg University Press, St. Petersburg, 1976). 
%
\end{thebibliography}

\newpage

\begin{table}[t]
\begin{center}
\begin{tabular}{|cccc|c|}
\,\,\,$L$ &
$n_1$ &
$n_2$ &
$n_3$ &
$W^{(L,n_1,n_2,n_3)}$
\\
\hline
$2$ & $0$ & $0$ & $2$ &
%
\begin{fmffile}{gl2002a}
%
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
% #1
%
${\displaystyle \frac{1}{2}}$
%
\parbox{7mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1w,1/2h}{v2}
\fmf{fermion,right=1}{v2,v1} 
\fmf{fermion,right=1}{v1,v2} 
\fmf{photon}{v2,v1}
\fmfdot{v2,v1}
\end{fmfgraph}\end{center}}
%
% #2
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1a}
\fmfforce{1/6w,0h}{v1b}
\fmfforce{1/3w,1/2h}{v2}
\fmfforce{2/3w,1/2h}{v3}
\fmfforce{5/6w,1h}{v4a}
\fmfforce{5/6w,0h}{v4b}
\fmf{fermion,right=1}{v1a,v1b} 
\fmf{plain,right=1}{v1b,v1a} 
\fmf{plain,right=1}{v1,v2}
\fmf{photon}{v2,v3}
\fmf{fermion,right=1}{v4b,v4a} 
\fmf{plain,right=1}{v4a,v4b}
\fmfdot{v2,v3}
\end{fmfgraph}\end{center}}
%
\end{fmffile}
%
\\ 
$2$ & $0$ & $1$ & $0$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl2010a}
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{1/4w,1h}{v1a}
\fmfforce{1/4w,0h}{v1b}
\fmfforce{1/2w,1/2h}{v2}
\fmfforce{1w,1/2h}{v3}
\fmf{fermion,right=1}{v1a,v1b} 
\fmf{plain,right=1}{v1b,v1a}
\fmf{photon,right=1}{v2,v3,v2}
\fmfdot{v2}
\end{fmfgraph}\end{center}}
%
\end{fmffile}
%
\\ 
$2$ & $1$ & $0$ & $0$ & 
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl2100a}
%
${\displaystyle \frac{1}{2}}$\,
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{1/4w,1h}{v1a}
\fmfforce{1/4w,0h}{v1b}
\fmfforce{1/2w,1/2h}{v2}
\fmfforce{3/4w,1h}{v3a}
\fmfforce{3/4w,0h}{v3b}
\fmf{fermion,right=1}{v1a,v1b} 
\fmf{plain,right=1}{v1b,v1a}
\fmf{plain,right=1}{v3a,v3b}
\fmf{fermion,right=1}{v3b,v3a}
\fmfdot{v2}
\end{fmfgraph}\end{center}}
%
\end{fmffile}
%
\\ \hline
$3$ & $0$ & $0$ & $4$ & 
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl3004a}
%
% #1
%
${\displaystyle \frac{1}{4}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,0h}{v1}
\fmfforce{1w,0h}{v2}
\fmfforce{1w,1h}{v3}
\fmfforce{0w,1h}{v4}
\fmf{fermion,right=0.4}{v1,v2}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=0.4}{v3,v4}
\fmf{fermion,right=0.4}{v4,v1}
\fmf{boson}{v1,v3}
\fmf{boson}{v2,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}\end{center}} 
%
% #2
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,0h}{v1}
\fmfforce{1w,0h}{v2}
\fmfforce{1w,1h}{v3}
\fmfforce{0w,1h}{v4}
\fmf{fermion,right=0.4}{v1,v2}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=0.4}{v3,v4}
\fmf{fermion,right=0.4}{v4,v1}
\fmf{boson,right=0.4}{v1,v4}
\fmf{boson,left=0.4}{v2,v3}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}\end{center}} 
%
% #3
%
${\displaystyle \frac{1}{4}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1}
\fmfforce{1/6w,0h}{v2}
\fmfforce{5/6w,1h}{v3}
\fmfforce{5/6w,0h}{v4}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson}{v1,v3}
\fmf{boson}{v2,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #4
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1}
\fmfforce{1/6w,0h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,1h}{v5}
\fmfforce{5/6w,0h}{v6}
\fmf{fermion,right=1}{v1,v2}
\fmf{plain,left=1}{v1,v2}
\fmf{boson}{v4,v3}
\fmf{boson}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{fermion,right=0.4}{v5,v4}
\fmf{fermion,right=0.4}{v4,v6}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #5
%
${\displaystyle \frac{1}{2}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,1h}{v1a}
\fmfforce{1/10w,0h}{v1b}
\fmfforce{1/5w,1/2h}{v2}
\fmfforce{2/5w,1/2h}{v3}
\fmfforce{3/5w,1/2h}{v4}
\fmfforce{4/5w,1/2h}{v5}
\fmfforce{9/10w,1h}{v6a}
\fmfforce{9/10w,0h}{v6b}
\fmf{fermion,right=1}{v1a,v1b}
\fmf{plain,right=1}{v1b,v1a}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v6b,v6a}
\fmf{plain,right=1}{v6a,v6b}
\fmf{boson}{v2,v3}
\fmf{boson}{v4,v5}
\fmfdot{v2,v3,v4,v5}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\
$3$ & $0$ & $1$ & $2$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl3012a}
%
% #1
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/2w,1/2h}{v2}
\fmfforce{3/4w,1h}{v3}
\fmfforce{3/4w,0h}{v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=0.4}{v2,v4}
\fmf{boson,left=1}{v2,v1,v2}
\fmf{boson}{v3,v4}
\fmfdot{v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #2
%
$1$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,6)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{1w,0.5h}{v2}
\fmfforce{1/2w,0h}{v3}
\fmfforce{0.12w,0.8h}{v4}
\fmfforce{0.88w,0.8h}{v5}
\fmf{fermion,right=0.5}{v5,v4}
\fmf{fermion,right=0.6}{v4,v3}
\fmf{fermion,right=0.6}{v3,v5}
\fmf{boson}{v3,v4}
\fmf{boson}{v3,v5}
\fmfdot{v3,v4,v5}
\end{fmfgraph}\end{center}} 
%
% #3
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1}
\fmfforce{1/6w,0h}{v2}
\fmfforce{2/3w,1/2h}{v3}
\fmfforce{5/6w,1h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{boson,left=0.2}{v1,v3}
\fmf{boson,right=0.2}{v2,v3}
\fmfdot{v1,v2,v3}
\end{fmfgraph}
\end{center}}
%
% #4
%
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/4w,1/2h}{v2}
\fmfforce{1/2w,1/2h}{v3}
\fmfforce{3/4w,1/2h}{v4}
\fmfforce{7/8w,1h}{v5a}
\fmfforce{7/8w,0h}{v5b}
\fmf{boson,left=1}{v1,v2,v1}
\fmf{fermion,right=1}{v3,v2}
\fmf{fermion,right=1}{v2,v3}
\fmf{boson}{v3,v4}
\fmf{fermion,right=1}{v5b,v5a}
\fmf{plain,right=1}{v5a,v5b}
\fmfdot{v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #5
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/3w,1/2h}{v2}
\fmfforce{2/3w,1/2h}{v3}
\fmfforce{5/6w,1h}{v4a}
\fmfforce{5/6w,0h}{v4b}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,left=1}{v2,v1}
\fmf{boson}{v1,v3}
\fmf{fermion,right=1}{v4b,v4a}
\fmf{plain,right=1}{v4a,v4b}
\fmfdot{v2,v3,v1}
\end{fmfgraph}
\end{center}}
%
% #6
%
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,6)
\setval
\fmfforce{1/8w,2/3h}{v1}
\fmfforce{1/8w,0h}{v2}
\fmfforce{1/4w,1/3h}{v3}
\fmfforce{2/4w,1/3h}{v4}
\fmfforce{3/8w,2/3h}{v5}
\fmfforce{5/8w,2/3h}{v6}
\fmfforce{3/4w,1/3h}{v7}
\fmfforce{7/8w,2/3h}{v8}
\fmfforce{7/8w,0h}{v9}
\fmf{fermion,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{boson}{v3,v4}
\fmf{fermion,right=1}{v6,v5}
\fmf{plain,right=1}{v5,v6}
\fmf{boson}{v4,v7}
\fmf{fermion,right=1}{v9,v8}
\fmf{plain,right=1}{v8,v9}
\fmfdot{v3,v4,v7}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\
$3$ & $0$ & $2$ & $0$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl3020a}
%
% #1
%
${\displaystyle \frac{1}{4}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,4)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{1w,0.5h}{v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{photon,left=0.4}{v1,v2,v1}
\fmfdot{v1,v2}
\end{fmfgraph}\end{center}} 
%
% #2
%
${\displaystyle \frac{1}{8}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/3w,1/2h}{v2}
\fmfforce{2/3w,1/2h}{v3}
\fmfforce{1w,1/2h}{v4}
\fmf{boson,left=1}{v1,v2,v1}
\fmf{boson,left=1}{v3,v4,v3}
\fmf{fermion,right=1}{v3,v2}
\fmf{fermion,right=1}{v2,v3}
\fmfdot{v2,v3}
\end{fmfgraph}
\end{center}}
%
% #3
%
${\displaystyle \frac{1}{4}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1a}
\fmfforce{1/6w,0h}{v1b}
\fmfforce{1/3w,1/2h}{v2}
\fmfforce{2/3w,1/2h}{v3}
\fmfforce{5/6w,1h}{v4a}
\fmfforce{5/6w,0h}{v4b}
\fmf{boson,left=1}{v2,v3,v2}
\fmf{fermion,right=1}{v1a,v1b}
\fmf{plain,right=1}{v1b,v1a}
\fmf{fermion,right=1}{v4b,v4a}
\fmf{plain,right=1}{v4a,v4b}
\fmfdot{v2,v3}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\
$3$ & $1$ & $0$ & $2$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl3102a}
%
% #1
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{1/4w,1h}{v1}
\fmfforce{1/4w,0h}{v2}
\fmfforce{1/2w,1/2h}{v3}
\fmfforce{3/4w,1h}{v4}
\fmfforce{3/4w,0h}{v5}
\fmf{boson}{v4,v5}
\fmf{fermion,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=0.4}{v4,v3}
\fmf{fermion,right=0.4}{v3,v5}
\fmfdot{v4,v5,v3}
\end{fmfgraph}
\end{center}}
%
% #2
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,6)
\setval
\fmfforce{0w,2/3h}{v1}
\fmfforce{1/2w,2/3h}{v2}
\fmfforce{1w,2/3h}{v3}
\fmf{boson,right=1}{v1,v3}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v3,v2}
\fmf{fermion,right=1}{v2,v3}
\fmfdot{v2,v3,v1}
\end{fmfgraph}
\end{center}}
%
% #3
%
$1$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{1/8w,1h}{v1a}
\fmfforce{1/8w,0h}{v1b}
\fmfforce{1/4w,1/2h}{v2}
\fmfforce{2/4w,1/2h}{v3}
\fmfforce{3/4w,1/2h}{v4}
\fmfforce{7/8w,1h}{v5a}
\fmfforce{7/8w,0h}{v5b}
\fmf{boson}{v4,v3}
\fmf{fermion,right=1}{v1a,v1b}
\fmf{plain,right=1}{v1b,v1a}
\fmf{fermion,right=1}{v3,v2}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v5b,v5a}
\fmf{plain,right=1}{v5a,v5b}
\fmfdot{v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\
$3$ & $1$ & $1$ & $0$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl3110a}
%
% #1
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/3w,1/2h}{v2}
\fmfforce{2/3w,1/2h}{v3}
\fmfforce{5/6w,1h}{v4a}
\fmfforce{5/6w,0h}{v4b}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=1}{v3,v2}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v4b,v4a}
\fmf{plain,right=1}{v4a,v4b}
\fmfdot{v2,v3}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\
$3$ & $2$ & $0$ & $0$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl3200a}
%
% #1
%
${\displaystyle \frac{1}{8}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,4)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{1w,0.5h}{v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,left=0.4}{v1,v2}
\fmf{fermion,left=0.4}{v2,v1}
\fmfdot{v1,v2}
\end{fmfgraph}\end{center}} 
%
% #2
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1a}
\fmfforce{1/6w,0h}{v1b}
\fmfforce{1/3w,1/2h}{v2}
\fmfforce{2/3w,1/2h}{v3}
\fmfforce{5/6w,1h}{v4a}
\fmfforce{5/6w,0h}{v4b}
\fmf{fermion,right=1}{v1a,v1b}
\fmf{plain,right=1}{v1b,v1a}
\fmf{fermion,right=1}{v3,v2}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v4b,v4a}
\fmf{plain,right=1}{v4a,v4b}
\fmfdot{v2,v3}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\ \hline
%
$4$ & $0$ & $0$ & $6$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4006a}
%
% #1
%
${\displaystyle \frac{1}{6}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,6)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{0.25w,0.933h}{v2}
\fmfforce{0.75w,0.933h}{v3}
\fmfforce{1w,0.5h}{v4}
\fmfforce{0.75w,0.067h}{v5}
\fmfforce{0.25w,0.067h}{v6}
\fmf{fermion,right=0.3}{v1,v6,v5,v4,v3,v2,v1}
\fmf{boson}{v1,v4}
\fmf{boson}{v2,v5}
\fmf{boson}{v3,v6}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #2
%
${\displaystyle \frac{1}{2}}$
% 
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,6)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{0.25w,0.933h}{v2}
\fmfforce{0.75w,0.933h}{v3}
\fmfforce{1w,0.5h}{v4}
\fmfforce{0.75w,0.067h}{v5}
\fmfforce{0.25w,0.067h}{v6}
\fmf{fermion,right=0.3}{v1,v6,v5,v4,v3,v2,v1}
\fmf{boson}{v1,v4}
\fmf{boson}{v2,v6}
\fmf{boson}{v3,v5}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
% 
% #3
%
${\displaystyle \frac{1}{6}}$
% 
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1}
\fmfforce{1/6w,0h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,1h}{v5}
\fmfforce{5/6w,0h}{v6}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{boson}{v3,v4}
\fmf{boson}{v1,v5}
\fmf{boson}{v2,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{fermion,right=0.4}{v5,v4}
\fmf{fermion,right=0.4}{v4,v6}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
% 
% #4
%
${\displaystyle \frac{1}{6}}$
% 
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1}
\fmfforce{1/6w,0h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,1h}{v5}
\fmfforce{5/6w,0h}{v6}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{boson}{v3,v4}
\fmf{boson}{v1,v5}
\fmf{boson}{v2,v6}
\fmf{fermion,left=1}{v5,v6}
\fmf{fermion,left=0.4}{v4,v5}
\fmf{fermion,left=0.4}{v6,v4}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
% 
% #5
%
${\displaystyle \frac{1}{3}}$
% 
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,6)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{0.25w,0.933h}{v2}
\fmfforce{0.75w,0.933h}{v3}
\fmfforce{1w,0.5h}{v4}
\fmfforce{0.75w,0.067h}{v5}
\fmfforce{0.25w,0.067h}{v6}
\fmf{fermion,right=0.3}{v1,v6,v5,v4,v3,v2,v1}
\fmf{boson,right=0.7}{v2,v3}
\fmf{boson,right=0.7}{v4,v5}
\fmf{boson,right=0.7}{v6,v1}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}} 
%
% #6
%
${\displaystyle \frac{1}{2}}$
% 
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,6)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{0.25w,0.933h}{v2}
\fmfforce{0.75w,0.933h}{v3}
\fmfforce{1w,0.5h}{v4}
\fmfforce{0.75w,0.067h}{v5}
\fmfforce{0.25w,0.067h}{v6}
\fmf{fermion,right=0.3}{v1,v6,v5,v4,v3,v2,v1}
\fmf{boson,right=0.7}{v2,v3}
\fmf{boson}{v1,v4}
\fmf{boson,right=0.7}{v5,v6}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #7
%
$1$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,6)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{0.25w,0.933h}{v2}
\fmfforce{0.75w,0.933h}{v3}
\fmfforce{1w,0.5h}{v4}
\fmfforce{0.75w,0.067h}{v5}
\fmfforce{0.25w,0.067h}{v6}
\fmf{fermion,right=0.3}{v1,v6,v5,v4,v3,v2,v1}
\fmf{boson,right=0.7}{v2,v3}
\fmf{boson,right=0.2}{v4,v6}
\fmf{boson,right=0.2}{v5,v1}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #8
%
 ${\displaystyle \frac{1}{2}}$
% 
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/6w,0h}{v3}
\fmfforce{1/3w,1/2h}{v4}
\fmfforce{5/6w,1h}{v5}
\fmfforce{5/6w,0h}{v6}
\fmf{fermion,right=0.4}{v1,v3,v4,v2,v1}
\fmf{boson}{v1,v4}
\fmf{boson}{v2,v5}
\fmf{boson}{v3,v6}
\fmf{fermion,right=1}{v5,v6,v5}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
\\
%
&&&&
%
\begin{fmffile}{gl4006b}
%
% #9
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1}
\fmfforce{1/6w,0h}{v2}
\fmfforce{0.03w,3/4h}{v3}
\fmfforce{0.03w,1/4h}{v4}
\fmfforce{5/6w,1h}{v5}
\fmfforce{5/6w,0h}{v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.3}{v1,v3,v4,v2}
\fmf{fermion,right=1}{v5,v6,v5}
\fmf{boson}{v1,v5}
\fmf{boson}{v2,v6}
\fmf{boson,left=0.7}{v3,v4}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #10
%
${\displaystyle \frac{1}{6}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/4w,0h}{v2}
\fmfforce{3/4w,0h}{v3}
\fmfforce{1w,1/2h}{v4}
\fmfforce{3/4w,1h}{v5}
\fmfforce{1/4w,1h}{v6}
\fmfforce{1/2w,1/2h}{v7}
\fmf{fermion,right=1}{v6,v5}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{boson}{v2,v3}
\fmf{boson}{v4,v5}
\fmf{boson}{v6,v1}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #11
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{0w,1/2h}{i1}
\fmfforce{1/3w,1/2h}{i2}
\fmfforce{0.045w,0.8h}{v1}
\fmfforce{0.045w,0.2h}{v2}
\fmfforce{0.23w,0.95h}{v3}
\fmfforce{0.23w,0.05h}{v4}
\fmfforce{1/3w,1/2h}{v5}
\fmfforce{2/3w,1/2h}{v6}
\fmfforce{5/6w,1h}{v7}
\fmfforce{5/6w,0h}{v8}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmf{fermion,right=0.3}{v5,v3}
\fmf{fermion,right=0.3}{v3,v1}
\fmf{fermion,right=0.3}{v1,v2}
\fmf{fermion,right=0.3}{v2,v4}
\fmf{fermion,right=0.3}{v4,v5}
\fmf{boson}{v6,v5}
\fmf{boson}{v1,v4}
\fmf{boson}{v2,v3}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #12
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{0w,1/2h}{i1}
\fmfforce{1/3w,1/2h}{i2}
\fmfforce{0.045w,0.8h}{v1}
\fmfforce{0.045w,0.2h}{v2}
\fmfforce{0.23w,0.95h}{v3}
\fmfforce{0.23w,0.05h}{v4}
\fmfforce{1/3w,1/2h}{v5}
\fmfforce{2/3w,1/2h}{v6}
\fmfforce{5/6w,1h}{v7}
\fmfforce{5/6w,0h}{v8}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmf{fermion,right=0.3}{v5,v3}
\fmf{fermion,right=0.3}{v3,v1}
\fmf{fermion,right=0.3}{v1,v2}
\fmf{fermion,right=0.3}{v2,v4}
\fmf{fermion,right=0.3}{v4,v5}
\fmf{boson}{v6,v5}
\fmf{boson}{v3,v4}
\fmf{boson,left=0.7}{v1,v2}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #13
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{0w,1/2h}{i1}
\fmfforce{1/3w,1/2h}{i2}
\fmfforce{0.045w,0.8h}{v1}
\fmfforce{0.045w,0.2h}{v2}
\fmfforce{0.23w,0.95h}{v3}
\fmfforce{0.23w,0.05h}{v4}
\fmfforce{1/3w,1/2h}{v5}
\fmfforce{2/3w,1/2h}{v6}
\fmfforce{5/6w,1h}{v7}
\fmfforce{5/6w,0h}{v8}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmf{fermion,right=0.3}{v5,v3}
\fmf{fermion,right=0.3}{v3,v1}
\fmf{fermion,right=0.3}{v1,v2}
\fmf{fermion,right=0.3}{v2,v4}
\fmf{fermion,right=0.3}{v4,v5}
\fmf{boson}{v6,v5}
\fmf{boson,left=0.7}{v3,v1}
\fmf{boson,left=0.7}{v2,v4}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #14
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,1h}{v1}
\fmfforce{1/6w,0h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,1h}{v5}
\fmfforce{5/6w,0h}{v6}
\fmf{boson}{v1,v2}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v6}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{fermion,right=1}{v6,v5}
\fmf{fermion,right=0.4}{v5,v4}
\fmf{fermion,right=0.4}{v4,v6}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #15
%
$1$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,1h}{v1}
\fmfforce{1/10w,0h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v6}
\fmfforce{5/10w,1h}{v4}
\fmfforce{5/10w,0h}{v5}
\fmfforce{9/10w,1h}{v7}
\fmfforce{9/10w,0h}{v8}
\fmf{boson}{v3,v6}
\fmf{boson}{v4,v7}
\fmf{boson}{v5,v8}
\fmf{fermion,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=0.4}{v4,v6}
\fmf{fermion,right=0.4}{v6,v5}
\fmf{fermion,right=1}{v8,v7}
\fmf{fermion,right=1}{v7,v8}
\fmfdot{v3,v4,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4006c}
%
% #16
%
${\displaystyle \frac{1}{2}}$
%
\parbox{22mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,1h}{v1}
\fmfforce{1/10w,0h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v4}
\fmfforce{5/10w,1h}{v5}
\fmfforce{5/10w,0h}{v6}
\fmfforce{3/5w,1/2h}{v7}
\fmfforce{4/5w,1/2h}{v8}
\fmfforce{9/10w,1h}{v9}
\fmfforce{9/10w,0h}{v10}
\fmf{fermion,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v5,v4,v6,v7,v5}
\fmf{fermion,right=1}{v10,v9}
\fmf{plain,right=1}{v9,v10}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v6}
\fmf{boson}{v7,v8}
\fmfdot{v3,v4,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}}
%
% #17
%
$1$
%
\parbox{22mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,1h}{v1}
\fmfforce{1/10w,0h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v4}
\fmfforce{0.447w,0.9h}{v5}
\fmfforce{0.553w,0.9h}{v6}
\fmfforce{3/5w,1/2h}{v7}
\fmfforce{4/5w,1/2h}{v8}
\fmfforce{9/10w,1h}{v9}
\fmfforce{9/10w,0h}{v10}
\fmf{fermion,right=1}{v4,v7}
\fmf{plain,left=1}{v7,v4}
\fmf{fermion,right=0.4}{v7,v6}
\fmf{fermion,right=0.4}{v6,v5}
\fmf{fermion,right=0.4}{v5,v4}
\fmf{fermion,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{fermion,right=1}{v10,v9}
\fmf{plain,right=1}{v9,v10}
\fmf{boson}{v3,v4}
\fmf{boson}{v7,v8}
\fmf{boson,right=0.7}{v5,v6}
\fmfdot{v3,v4,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}}
%
% #18
%
$1$
% 
\parbox{22mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,1h}{v1}
\fmfforce{1/10w,0h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v4}
\fmfforce{3/5w,1/2h}{v5}
\fmfforce{4/5w,1/2h}{v6}
\fmfforce{9/10w,1h}{v7}
\fmfforce{9/10w,0h}{v8}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmf{boson}{v1,v2}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v6}
\fmfdot{v1,v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #19
%
${\displaystyle \frac{1}{2}}$
% 
\parbox{30mm}{\begin{center}
\begin{fmfgraph}(28,4)
\setval
\fmfforce{1/14w,1h}{v1}
\fmfforce{1/14w,0h}{v2}
\fmfforce{1/7w,1/2h}{v3}
\fmfforce{2/7w,1/2h}{v4}
\fmfforce{3/7w,1/2h}{v5}
\fmfforce{4/7w,1/2h}{v6}
\fmfforce{5/7w,1/2h}{v7}
\fmfforce{6/7w,1/2h}{v8}
\fmfforce{13/14w,1h}{v9}
\fmfforce{13/14w,0h}{v10}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v6}
\fmf{boson}{v7,v8}
\fmf{fermion,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\fmf{fermion,right=1}{v10,v9}
\fmf{plain,right=1}{v9,v10}
\fmfdot{v3,v4,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}}
%
% #20
% 
${\displaystyle \frac{1}{3}}$
% 
\parbox{22mm}{\begin{center}
\begin{fmfgraph}(20,12)
\setval
\fmfforce{1/10w,1/3h}{v1}
\fmfforce{1/10w,0h}{v2}
\fmfforce{1/5w,1/6h}{v3}
\fmfforce{2/5w,1/6h}{v4}
\fmfforce{3/5w,1/6h}{v5}
\fmfforce{4/5w,1/6h}{v6}
\fmfforce{9/10w,1/3h}{v7}
\fmfforce{9/10w,0h}{v8}
\fmfforce{1/2w,1/3h}{v9}
\fmfforce{1/2w,2/3h}{v10}
\fmfforce{2/5w,5/6h}{v11}
\fmfforce{3/5w,5/6h}{v12}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v6}
\fmf{boson}{v9,v10}
\fmf{fermion,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=0.4}{v5,v9}
\fmf{fermion,right=0.4}{v9,v4}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmf{fermion,right=1}{v12,v11}
\fmf{plain,right=1}{v11,v12}
\fmfdot{v3,v4,v5,v6,v9,v10}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\
%
$4$ & $0$ & $1$ & $4$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4014a}
%
% #1
%
${\displaystyle \frac{1}{2}}$
%
\parbox{13mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{2/10w,0h}{v1}
\fmfforce{2/10w,1h}{v2}
\fmfforce{4/10w,1/2h}{v3}
\fmfforce{8/10w,0h}{v4}
\fmfforce{8/10w,1h}{v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{boson}{v1,v2}
\fmf{boson,left=0.6}{v3,v5}
\fmf{boson,left=0.6}{v4,v3}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}}
%
% #2
%
${\displaystyle \frac{1}{2}}$
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(14,4)
\setval
\fmfforce{0/14w,1/2h}{v1}
\fmfforce{4/14w,1/2h}{v2}
\fmfforce{6/14w,0h}{v3}
\fmfforce{6/14w,1h}{v4}
\fmfforce{12/14w,0h}{v5}
\fmfforce{12/14w,1h}{v6}
\fmf{boson,right=0.6}{v3,v5}
\fmf{boson,right=0.6}{v6,v4}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=0.4}{v4,v2}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmfdot{v2,v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #3
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{1/2w,0h}{v1}
\fmfforce{1/2w,6/10h}{v2}
\fmfforce{1/6w,8/10h}{v3}
\fmfforce{5/6w,8/10h}{v4}
\fmfforce{0.9/6w,1/10h}{v5}
\fmfforce{0.9/6w,5/10h}{v6}
\fmfforce{5.1/6w,1/10h}{v7}
\fmfforce{5.1/6w,5/10h}{v8}
\fmf{fermion,right=0.2}{v8,v2}
\fmf{fermion,right=0.2}{v2,v6}
\fmf{fermion,right=0.45}{v6,v5}
\fmf{fermion,right=0.45}{v5,v7}
\fmf{fermion,right=0.45}{v7,v8}
\fmf{boson,right=1}{v4,v3,v4}
\fmf{boson,left=0.45}{v7,v8}
\fmf{boson,right=0.45}{v5,v6}
\fmfdot{v2,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #4
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{1/2w,0h}{v1}
\fmfforce{1/2w,6/10h}{v2}
\fmfforce{1/6w,8/10h}{v3}
\fmfforce{5/6w,8/10h}{v4}
\fmfforce{0.9/6w,1/10h}{v5}
\fmfforce{0.9/6w,5/10h}{v6}
\fmfforce{5.1/6w,1/10h}{v7}
\fmfforce{5.1/6w,5/10h}{v8}
\fmf{fermion,right=0.2}{v8,v2}
\fmf{fermion,right=0.2}{v2,v6}
\fmf{fermion,right=0.45}{v6,v5}
\fmf{fermion,right=0.45}{v5,v7}
\fmf{fermion,right=0.45}{v7,v8}
\fmf{boson,left=1}{v4,v3,v4}
\fmf{boson,right=0.45}{v7,v5}
\fmf{boson,left=0.45}{v8,v6}
\fmfdot{v2,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #5
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{1/2w,0h}{v1}
\fmfforce{1/2w,6/10h}{v2}
\fmfforce{1/6w,8/10h}{v3}
\fmfforce{5/6w,8/10h}{v4}
\fmfforce{0.9/6w,1/10h}{v5}
\fmfforce{0.9/6w,5/10h}{v6}
\fmfforce{5.1/6w,1/10h}{v7}
\fmfforce{5.1/6w,5/10h}{v8}
\fmf{fermion,right=0.2}{v8,v2}
\fmf{fermion,right=0.2}{v2,v6}
\fmf{fermion,right=0.45}{v6,v5}
\fmf{fermion,right=0.45}{v5,v7}
\fmf{fermion,right=0.45}{v7,v8}
\fmf{boson,right=1}{v4,v3,v4}
\fmf{boson}{v7,v6}
\fmf{boson}{v8,v5}
\fmfdot{v2,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #6
%
${\displaystyle \frac{1}{2}}$
%
\parbox{13mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{0/10w,0h}{v1}
\fmfforce{0/10w,1h}{v2}
\fmfforce{4/10w,0h}{v3}
\fmfforce{4/10w,1h}{v4}
\fmfforce{6/10w,1/2h}{v5}
\fmfforce{8/10w,0h}{v6}
\fmfforce{8/10w,1h}{v7}
\fmf{fermion,right=1}{v6,v7}
\fmf{plain,right=1}{v7,v6}
\fmf{fermion,right=0.4}{v2,v1}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{fermion,right=0.4}{v3,v4}
\fmf{fermion,right=0.4}{v4,v2}
\fmf{boson,left=0.6}{v4,v5}
\fmf{boson,left=0.6}{v5,v3}
\fmf{boson,right=0.4}{v1,v2}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}}   
%
% #7
%
${\displaystyle \frac{1}{2}}$
%
\parbox{13mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{0/10w,1/2h}{v1}
\fmfforce{2/10w,0h}{v2}
\fmfforce{2/10w,1h}{v3}
\fmfforce{4/10w,1/2h}{v4}
\fmfforce{6/10w,1/2h}{v5}
\fmfforce{8/10w,0h}{v6}
\fmfforce{8/10w,1h}{v7}
\fmf{fermion,right=1}{v6,v7}
\fmf{plain,right=1}{v7,v6}
\fmf{fermion,right=0.4}{v1,v2}
\fmf{fermion,right=0.4}{v2,v4}
\fmf{fermion,right=0.4}{v4,v3}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{boson,right=0.6}{v2,v5}
\fmf{boson,right=0.6}{v5,v3}
\fmf{boson}{v1,v4}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #8
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,10)
\setval
\fmfforce{2/12w,0h}{v1}
\fmfforce{2/12w,4/10h}{v2}
\fmfforce{4/12w,2/10h}{v3}
\fmfforce{8/12w,2/10h}{v4}
\fmfforce{10/12w,0h}{v5}
\fmfforce{10/12w,4/10h}{v6}
\fmfforce{6/12w,6/10h}{v7}
\fmfforce{4/12w,8/10h}{v8}
\fmfforce{8/12w,8/10h}{v9}
\fmf{fermion,right=1}{v9,v8}
\fmf{plain,right=1}{v8,v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{plain,left=0.4}{v3,v1}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{plain,left=0.4}{v5,v4}
\fmf{boson,right=0.4}{v7,v2}
\fmf{boson,right=0.4}{v6,v7}
\fmf{boson}{v3,v4}
\fmfdot{v2,v3,v4,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #9
%
$1$
%
\parbox{13mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{2/10w,0h}{v2}
\fmfforce{2/10w,1h}{v3}
\fmfforce{8/10w,0h}{v4}
\fmfforce{8/10w,1h}{v5}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{fermion,right=0.4}{v1,v2}
\fmf{boson,left=0.6}{v3,v5}
\fmf{boson,left=0.4}{v3,v1}
\fmf{boson,left=0.6}{v4,v2}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4014b}
%
% #10
%
$1$
%
\parbox{13mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{4/10w,1/2h}{v2}
\fmfforce{8/10w,0h}{v3}
\fmfforce{8/10w,1h}{v4}
\fmfforce{10/10w,1/2h}{v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=0.4}{v3,v5}
\fmf{fermion,right=0.4}{v5,v4}
\fmf{boson,right=0.6}{v2,v3}
\fmf{boson,right=0.6}{v4,v2}
\fmf{boson,left=1}{v1,v5}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #11
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{1/2w,1h}{v1}
\fmfforce{7.8/8w,5.236/8h}{v2}
\fmfforce{6.35/8w,0.7639/8h}{v3}
\fmfforce{1.65/8w,0.7639/8h}{v4}
\fmfforce{0.2/8w,5.236/8h}{v5}
\fmfforce{1/2w,0h}{v6}
\fmf{fermion,right=0.35}{v2,v1}
\fmf{fermion,right=0.35}{v1,v5}
\fmf{fermion,right=0.35}{v5,v4}
\fmf{fermion,right=0.35}{v4,v3}
\fmf{fermion,right=0.35}{v3,v2}
\fmf{boson,left=0.35}{v2,v1}
\fmf{boson}{v3,v5}
\fmf{boson}{v4,v2}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #12
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{1/2w,1h}{v1}
\fmfforce{7.8/8w,5.236/8h}{v2}
\fmfforce{6.35/8w,0.7639/8h}{v3}
\fmfforce{1.65/8w,0.7639/8h}{v4}
\fmfforce{0.2/8w,5.236/8h}{v5}
\fmfforce{1/2w,0h}{v6}
\fmf{fermion,right=0.35}{v2,v1}
\fmf{fermion,right=0.35}{v1,v5}
\fmf{fermion,right=0.35}{v5,v4}
\fmf{fermion,right=0.35}{v4,v3}
\fmf{fermion,right=0.35}{v3,v2}
\fmf{boson,left=0.35}{v1,v5}
\fmf{boson}{v3,v5}
\fmf{boson}{v4,v2}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #13
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{1/2w,1h}{v1}
\fmfforce{7.8/8w,5.236/8h}{v2}
\fmfforce{6.35/8w,0.7639/8h}{v3}
\fmfforce{1.65/8w,0.7639/8h}{v4}
\fmfforce{0.2/8w,5.236/8h}{v5}
\fmfforce{1/2w,0h}{v6}
\fmf{fermion,right=0.35}{v2,v1}
\fmf{fermion,right=0.35}{v1,v5}
\fmf{fermion,right=0.35}{v5,v4}
\fmf{fermion,right=0.35}{v4,v3}
\fmf{fermion,right=0.35}{v3,v2}
\fmf{boson}{v2,v5}
\fmf{boson}{v1,v4}
\fmf{boson}{v3,v1}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #14
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{1/2w,1h}{v1}
\fmfforce{7.8/8w,5.236/8h}{v2}
\fmfforce{6.35/8w,0.7639/8h}{v3}
\fmfforce{1.65/8w,0.7639/8h}{v4}
\fmfforce{0.2/8w,5.236/8h}{v5}
\fmfforce{1/2w,0h}{v6}
\fmf{fermion,right=0.35}{v2,v1}
\fmf{fermion,right=0.35}{v1,v5}
\fmf{fermion,right=0.35}{v5,v4}
\fmf{fermion,right=0.35}{v4,v3}
\fmf{fermion,right=0.35}{v3,v2}
\fmf{boson,left=0.35}{v1,v5}
\fmf{boson,left=0.35}{v5,v4}
\fmf{boson,left=0.35}{v3,v2}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #15
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{1/2w,1h}{v1}
\fmfforce{7.8/8w,5.236/8h}{v2}
\fmfforce{6.35/8w,0.7639/8h}{v3}
\fmfforce{1.65/8w,0.7639/8h}{v4}
\fmfforce{0.2/8w,5.236/8h}{v5}
\fmfforce{1/2w,0h}{v6}
\fmf{fermion,right=0.35}{v2,v1}
\fmf{fermion,right=0.35}{v1,v5}
\fmf{fermion,right=0.35}{v5,v4}
\fmf{fermion,right=0.35}{v4,v3}
\fmf{fermion,right=0.35}{v3,v2}
\fmf{boson,left=0.35}{v5,v4}
\fmf{boson}{v5,v3}
\fmf{boson,left=0.35}{v2,v1}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #16
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{1/2w,1h}{v1}
\fmfforce{7.8/8w,5.236/8h}{v2}
\fmfforce{6.35/8w,0.7639/8h}{v3}
\fmfforce{1.65/8w,0.7639/8h}{v4}
\fmfforce{0.2/8w,5.236/8h}{v5}
\fmfforce{1/2w,0h}{v6}
\fmf{fermion,right=0.35}{v2,v1}
\fmf{fermion,right=0.35}{v1,v5}
\fmf{fermion,right=0.35}{v5,v4}
\fmf{fermion,right=0.35}{v4,v3}
\fmf{fermion,right=0.35}{v3,v2}
\fmf{boson,left=0.35}{v1,v5}
\fmf{boson}{v5,v2}
\fmf{boson,left=0.35}{v4,v3}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #17
%
$1$
%
\parbox{13mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{2/10w,0h}{v2}
\fmfforce{2/10w,1h}{v3}
\fmfforce{8/10w,0h}{v4}
\fmfforce{8/10w,1h}{v5}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{fermion,right=0.4}{v1,v2}
\fmf{boson,left=0.6}{v3,v5}
\fmf{boson,left=0.4}{v1,v2}
\fmf{boson,left=0.6}{v4,v2}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4014c}
%
% #18
%
$1$
%
\parbox{21mm}{\begin{center}
\begin{fmfgraph}(18,4)
\setval
\fmfforce{2/18w,0h}{v1}
\fmfforce{2/18w,1h}{v2}
\fmfforce{4/18w,1/2h}{v3}
\fmfforce{8/18w,0h}{v4}
\fmfforce{8/18w,1h}{v5}
\fmfforce{10/18w,1/2h}{v6}
\fmfforce{14/18w,1/2h}{v7}
\fmfforce{16/18w,0h}{v8}
\fmfforce{16/18w,1h}{v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v8,v9}
\fmf{plain,right=1}{v9,v8}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=0.4}{v4,v6}
\fmf{fermion,right=0.4}{v6,v5}
\fmf{boson,right=0.6}{v3,v4}
\fmf{boson,right=0.6}{v5,v3}
\fmf{boson}{v6,v7}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #19
%
$1$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{2/20w,0h}{v1}
\fmfforce{2/20w,1h}{v2}
\fmfforce{4/20w,1/2h}{v3}
\fmfforce{8/20w,1/2h}{v4}
\fmfforce{12/20w,1/2h}{v5}
\fmfforce{16/20w,1/2h}{v6}
\fmfforce{20/20w,1/2h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v6}
\fmf{boson,left=1}{v4,v7}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #20
%
${\displaystyle \frac{1}{2}}$
%
\parbox{21mm}{\begin{center}
\begin{fmfgraph}(18,4)
\setval
\fmfforce{2/18w,0h}{v1}
\fmfforce{2/18w,1h}{v2}
\fmfforce{4/18w,1/2h}{v3}
\fmfforce{8/18w,1/2h}{v4}
\fmfforce{12/18w,1/2h}{v5}
\fmfforce{16/18w,0h}{v6}
\fmfforce{16/18w,1h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\fmf{boson}{v3,v4}
\fmf{boson,right=0.6}{v5,v6}
\fmf{boson,right=0.6}{v7,v5}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}}
%
% #21
%
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,1h}{v2}
\fmfforce{4/16w,1/2h}{v3}
\fmfforce{8/16w,1/2h}{v4}
\fmfforce{12/16w,1/2h}{v5}
\fmfforce{1w,1/2h}{v6}
\fmfforce{14/16w,0h}{v7}
\fmfforce{14/16w,1h}{v8}
\fmf{boson}{v7,v8}
\fmf{boson}{v4,v5}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v7,v8}
\fmf{fermion,right=0.4}{v8,v5}
\fmf{fermion,right=0.4}{v5,v7}
\fmfdot{v3,v4,v5,v7,v8}
\end{fmfgraph}\end{center}} 
%
% #22
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{2/12w,0h}{v1}
\fmfforce{2/12w,1h}{v2}
\fmfforce{4/12w,1/2h}{v3}
\fmfforce{8/12w,1/2h}{v4}
\fmfforce{12/12w,1/2h}{v5}
\fmf{boson}{v1,v2}
\fmf{boson}{v3,v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.5}{v1,v3}
\fmf{fermion,right=0.5}{v3,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}\end{center}} 
%
% #23
%
${\displaystyle \frac{1}{2}}$
%
\parbox{21mm}{\begin{center}
\begin{fmfgraph}(18,6)
\setval
\fmfforce{2/18w,0h}{v1}
\fmfforce{2/18w,2/3h}{v2}
\fmfforce{4/18w,1/3h}{v3}
\fmfforce{8/18w,1/3h}{v4}
\fmfforce{14/18w,1/3h}{v5}
\fmfforce{18/18w,1/3h}{v6}
\fmfforce{9.5/18w,4.5/6h}{v7}
\fmfforce{12.5/18w,4.5/6h}{v8}
\fmf{boson}{v3,v4}
\fmf{boson,right=0.6}{v7,v8}
\fmf{boson,right=1}{v5,v6,v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=0.3}{v5,v8}
\fmf{fermion,right=0.3}{v8,v7}
\fmf{fermion,right=0.3}{v7,v4}
\fmfdot{v3,v4,v5,v7,v8}
\end{fmfgraph}\end{center}} 
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4014d}
%
% #24
%
${\displaystyle \frac{1}{2}}$
%
\parbox{21mm}{\begin{center}
\begin{fmfgraph}(18,6)
\setval
\fmfforce{0/18w,1/3h}{v1}
\fmfforce{4/18w,1/3h}{v2}
\fmfforce{10/18w,1/3h}{v3}
\fmfforce{14/18w,1/3h}{v4}
\fmfforce{16/18w,0h}{v5}
\fmfforce{16/18w,2/3h}{v6}
\fmfforce{5.5/18w,4.5/6h}{v7}
\fmfforce{8.5/18w,4.5/6h}{v8}
\fmf{boson}{v3,v4}
\fmf{boson,right=0.6}{v7,v8}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,right=1}{v6,v5}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=0.3}{v3,v8}
\fmf{fermion,right=0.3}{v8,v7}
\fmf{fermion,right=0.3}{v7,v2}
\fmfdot{v2,v3,v4,v7,v8}
\end{fmfgraph}\end{center}} 
%
% #25
%
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,1h}{v2}
\fmfforce{4/16w,1/2h}{v3}
\fmfforce{8/16w,1/2h}{v4}
\fmfforce{10/16w,0h}{v5}
\fmfforce{10/16w,1h}{v6}
\fmfforce{12/16w,1/2h}{v7}
\fmfforce{16/16w,1/2h}{v8}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v6}
\fmf{boson,right=1}{v7,v8,v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v4,v5}
\fmf{fermion,right=0.4}{v5,v7}
\fmf{fermion,right=0.4}{v7,v6}
\fmf{fermion,right=0.4}{v6,v4}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}\end{center}} 
%
% #26
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{2/12w,0h}{v1}
\fmfforce{2/12w,1h}{v2}
\fmfforce{4/12w,1/2h}{v3}
\fmfforce{8/12w,1/2h}{v4}
\fmfforce{10/12w,0h}{v5}
\fmfforce{10/12w,1h}{v6}
\fmfforce{12/12w,1/2h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v7,v6}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{fermion,right=0.4}{v4,v5}
\fmf{fermion,right=0.4}{v5,v7}
\fmf{boson,right=0.4}{v6,v7}
\fmf{boson,left=0.4}{v4,v5}
\fmf{boson}{v3,v4}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #27
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{2/12w,0h}{v1}
\fmfforce{2/12w,1h}{v2}
\fmfforce{4/12w,1/2h}{v3}
\fmfforce{8/12w,1/2h}{v4}
\fmfforce{10/12w,0h}{v5}
\fmfforce{10/12w,1h}{v6}
\fmfforce{12/12w,1/2h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v7,v6}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{fermion,right=0.4}{v4,v5}
\fmf{fermion,right=0.4}{v5,v7}
\fmf{boson,left=0.4}{v6,v4}
\fmf{boson,right=0.4}{v7,v5}
\fmf{boson}{v3,v4}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #28
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{2/12w,0h}{v1}
\fmfforce{2/12w,1h}{v2}
\fmfforce{4/12w,1/2h}{v3}
\fmfforce{8/12w,1/2h}{v4}
\fmfforce{10/12w,0h}{v5}
\fmfforce{10/12w,1h}{v6}
\fmfforce{12/12w,1/2h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v7,v6}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{fermion,right=0.4}{v4,v5}
\fmf{fermion,right=0.4}{v5,v7}
\fmf{boson}{v6,v5}
\fmf{boson}{v7,v4}
\fmf{boson}{v3,v4}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #29
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{2/12w,0h}{v1}
\fmfforce{2/12w,1h}{v2}
\fmfforce{4/12w,1/2h}{v3}
\fmfforce{8/12w,1/2h}{v4}
\fmfforce{10/12w,0h}{v5}
\fmfforce{10/12w,1h}{v6}
\fmfforce{12/12w,1/2h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v7,v6}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{fermion,right=0.4}{v4,v5}
\fmf{fermion,right=0.4}{v5,v7}
\fmf{boson}{v6,v5}
\fmf{boson,left=0.4}{v7,v6}
\fmf{boson}{v3,v4}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4014e}
%
% #30
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{2/12w,0h}{v1}
\fmfforce{2/12w,1h}{v2}
\fmfforce{4/12w,1/2h}{v3}
\fmfforce{8/12w,1/2h}{v4}
\fmfforce{10/12w,0h}{v5}
\fmfforce{10/12w,1h}{v6}
\fmfforce{12/12w,1/2h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v7,v6}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{fermion,right=0.4}{v4,v5}
\fmf{fermion,right=0.4}{v5,v7}
\fmf{boson}{v6,v5}
\fmf{boson,right=0.4}{v7,v5}
\fmf{boson}{v3,v4}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #31
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{2/12w,0h}{v1}
\fmfforce{2/12w,1h}{v2}
\fmfforce{4/12w,1/2h}{v3}
\fmfforce{8/12w,1/2h}{v4}
\fmfforce{10/12w,0h}{v5}
\fmfforce{10/12w,1h}{v6}
\fmfforce{12/12w,1/2h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v7,v6}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{fermion,right=0.4}{v4,v5}
\fmf{fermion,right=0.4}{v5,v7}
\fmf{boson,right=0.4}{v6,v7}
\fmf{boson,right=0.4}{v7,v5}
\fmf{boson}{v3,v4}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #32
%
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,6)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,2/3h}{v2}
\fmfforce{4/16w,1/3h}{v3}
\fmfforce{8/16w,1/3h}{v4}
\fmfforce{12/16w,1/3h}{v5}
\fmfforce{14/16w,0h}{v6}
\fmfforce{14/16w,2/3h}{v7}
\fmfforce{6/16w,2/3h}{v8}
\fmfforce{10/16w,2/3h}{v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v6,v7}
\fmf{plain,right=1}{v7,v6}
\fmf{fermion,right=1}{v9,v8}
\fmf{fermion,right=0.4}{v4,v9}
\fmf{fermion,right=0.4}{v8,v4}
\fmf{boson}{v3,v5}
\fmf{boson}{v8,v9}
\fmfdot{v3,v4,v5,v8,v9}
\end{fmfgraph}
\end{center}}
%
% #33
%
${\displaystyle \frac{1}{2}}$
%
\parbox{27mm}{\begin{center}
\begin{fmfgraph}(24,4)
\setval
\fmfforce{2/24w,0h}{v1}
\fmfforce{2/24w,1h}{v2}
\fmfforce{4/24w,1/2h}{v3}
\fmfforce{8/24w,1/2h}{v4}
\fmfforce{12/24w,1/2h}{v5}
\fmfforce{16/24w,1/2h}{v6}
\fmfforce{20/24w,1/2h}{v7}
\fmfforce{24/24w,1/2h}{v8}
\fmf{boson}{v3,v4}
\fmf{boson}{v6,v5}
\fmf{boson,right=1}{v7,v8,v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}\end{center}} 
%
% #34
%
$1$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{2/20w,0h}{v1}
\fmfforce{2/20w,1h}{v2}
\fmfforce{4/20w,1/2h}{v3}
\fmfforce{8/20w,1/2h}{v4}
\fmfforce{12/20w,1/2h}{v5}
\fmfforce{16/20w,1/2h}{v6}
\fmfforce{20/20w,1/2h}{v7}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\fmfdot{v6,v7,v3,v4,v5}
\end{fmfgraph}\end{center}} 
%
% #35
%
$1$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,6)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,2/3h}{v2}
\fmfforce{4/16w,1/3h}{v3}
\fmfforce{8/16w,1/3h}{v4}
\fmfforce{6/16w,2/3h}{v5}
\fmfforce{10/16w,2/3h}{v6}
\fmfforce{12/16w,1/3h}{v7}
\fmfforce{14/16w,0h}{v8}
\fmfforce{14/16w,2/3h}{v9}
\fmf{boson}{v1,v2}
\fmf{boson}{v3,v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=1}{v6,v5}
\fmf{plain,right=1}{v5,v6}
\fmf{fermion,right=1}{v8,v9}
\fmf{plain,right=1}{v9,v8}
\fmfdot{v1,v2,v3,v4,v7}
\end{fmfgraph}\end{center}} 
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4014f}
%
% #36
%
${\displaystyle \frac{1}{2}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,8)
\setval
\fmfforce{2/20w,0h}{v1}
\fmfforce{2/20w,1/2h}{v2}
\fmfforce{4/20w,1/4h}{v3}
\fmfforce{8/20w,1/4h}{v4}
\fmfforce{12/20w,1/4h}{v5}
\fmfforce{10/20w,1/2h}{v6}
\fmfforce{10/20w,1h}{v7}
\fmfforce{16/20w,1/4h}{v8}
\fmfforce{18/20w,0h}{v9}
\fmfforce{18/20w,1/2h}{v10}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v8}
\fmf{boson,right=1}{v6,v7,v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=0.4}{v5,v6}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{fermion,right=1}{v9,v10}
\fmf{plain,right=1}{v10,v9}
\fmfdot{v3,v4,v5,v8,v6}
\end{fmfgraph}\end{center}} 
%
% #37
%
$1$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{2/20w,0h}{v1}
\fmfforce{2/20w,1h}{v2}
\fmfforce{4/20w,1/2h}{v3}
\fmfforce{8/20w,1/2h}{v4}
\fmfforce{10/20w,1h}{v5}
\fmfforce{12/20w,1/2h}{v6}
\fmfforce{16/20w,1/2h}{v7}
\fmfforce{18/20w,0h}{v8}
\fmfforce{18/20w,1h}{v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v6}
\fmf{fermion,right=0.4}{v6,v5}
\fmf{fermion,right=0.4}{v5,v4}
\fmf{fermion,right=1}{v8,v9}
\fmf{plain,right=1}{v9,v8}
\fmf{boson}{v3,v4}
\fmf{boson}{v7,v6}
\fmf{boson,right=0.4}{v4,v5}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #38
%
$1$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{2/20w,0h}{v1}
\fmfforce{2/20w,1h}{v2}
\fmfforce{4/20w,1/2h}{v3}
\fmfforce{8/20w,1/2h}{v4}
\fmfforce{10/20w,0h}{v5}
\fmfforce{12/20w,1/2h}{v6}
\fmfforce{16/20w,1/2h}{v7}
\fmfforce{18/20w,0h}{v8}
\fmfforce{18/20w,1h}{v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v6,v4}
\fmf{fermion,right=0.4}{v5,v6}
\fmf{fermion,right=0.4}{v4,v5}
\fmf{fermion,right=1}{v8,v9}
\fmf{plain,right=1}{v9,v8}
\fmf{boson}{v3,v4}
\fmf{boson}{v7,v6}
\fmf{boson,left=0.4}{v4,v5}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #39
%
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,14)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,4/14h}{v2}
\fmfforce{4/16w,2/14h}{v3}
\fmfforce{8/16w,2/14h}{v4}
\fmfforce{12/16w,2/14h}{v5}
\fmfforce{14/16w,0h}{v6}
\fmfforce{14/16w,4/14h}{v7}
\fmfforce{8/16w,6/14h}{v8}
\fmfforce{8/16w,10/14h}{v9}
\fmfforce{6/16w,12/14h}{v10}
\fmfforce{10/16w,12/14h}{v11}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v6,v7}
\fmf{plain,right=1}{v7,v6}
\fmf{fermion,right=1}{v4,v8}
\fmf{fermion,right=1}{v8,v4}
\fmf{fermion,right=1}{v11,v10}
\fmf{plain,right=1}{v10,v11}
\fmf{boson}{v3,v5}
\fmf{boson}{v9,v8}
\fmfdot{v3,v4,v5,v8,v9}
\end{fmfgraph}
\end{center}}
%
% #40
%
$1$
%
\parbox{27mm}{\begin{center}
\begin{fmfgraph}(24,6)
\setval
\fmfforce{2/24w,0h}{v1}
\fmfforce{2/24w,2/3h}{v2}
\fmfforce{4/24w,1/3h}{v3}
\fmfforce{8/24w,1/3h}{v4}
\fmfforce{12/24w,1/3h}{v5}
\fmfforce{16/24w,1/3h}{v6}
\fmfforce{14/24w,2/3h}{v7}
\fmfforce{18/24w,2/3h}{v8}
\fmfforce{20/24w,1/3h}{v9}
\fmfforce{22/24w,0h}{v10}
\fmfforce{22/24w,2/3h}{v11}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{plain,right=1}{v7,v8}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v11,v10}
\fmf{fermion,right=1}{v10,v11}
\fmfdot{v3,v4,v5,v6,v9}
\end{fmfgraph}\end{center}} 
%
\end{fmffile}
%
\\
%
$4$ & $0$ & $2$ & $2$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4022a}
%
% #1
%
${\displaystyle \frac{1}{4}}$
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(14,4)
\setval
\fmfforce{2/14w,0h}{v1}
\fmfforce{2/14w,1h}{v2}
\fmfforce{4/14w,1/2h}{v3}
\fmfforce{8/14w,1/2h}{v4}
\fmfforce{10/14w,1/2h}{v5}
\fmfforce{12/14w,0h}{v6}
\fmfforce{12/14w,1h}{v7}
\fmfforce{12/14w,1/2h}{v8}
\fmfforce{1w,1/2h}{v9}
\fmfdot{v3,v4,v6,v7}
\fmf{boson,left}{v2,v1}
\fmf{boson,right=1}{v2,v1}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson,right=0.5}{v4,v6}
\fmf{boson,left=0.5}{v4,v7}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\end{fmfgraph}
\end{center}} 
%
% #2
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmf{boson}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{boson,right=1}{v4,v3,v4}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,right=1}{v6,v5}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #3
%
${\displaystyle \frac{1}{4}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,4)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{1w,0.5h}{v2}
\fmfforce{1/2w,1.25h}{v3}
\fmfforce{1/2w,-0.25h}{v4}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{fermion,right=0.4}{v4,v2}
\fmf{fermion,right=0.4}{v1,v4}
\fmf{boson,right=0.4}{v1,v2,v1}
\fmf{boson,left=0.4}{v3,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}\end{center}} 
%
% #4
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,4)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{1w,0.5h}{v2}
\fmfforce{1/4w,1.14h}{v3}
\fmfforce{3/4w,1.14h}{v4}
\fmf{boson,left=0.3}{v4,v3}
\fmf{fermion,right=0.3}{v2,v4}
\fmf{fermion,right=0.3}{v4,v3}
\fmf{fermion,right=0.3}{v3,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{boson,left=0.4}{v2,v1,v2}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}\end{center}} 
%
% #5
%
${\displaystyle \frac{1}{4}}$
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(14,6)
\setval
\fmfforce{2/14w,1/6h}{v1}
\fmfforce{2/14w,5/6h}{v2}
\fmfforce{4/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4}
\fmfforce{12/14w,1/6h}{v5}
\fmfforce{12/14w,5/6h}{v6}
\fmfforce{5/14w,0.9h}{v7}
\fmfforce{9/14w,0.9h}{v8}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=0.32}{v4,v8}
\fmf{fermion,right=0.32}{v8,v7}
\fmf{boson,left=0.4}{v8,v7}
\fmf{fermion,right=0.25}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson,left=1}{v5,v6,v5}
\fmfdot{v3,v4,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #6
%
${\displaystyle \frac{1}{4}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmfforce{1/2w,1h}{v7}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{boson,left=0.5}{v2,v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{boson,right=1}{v4,v3,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v6,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #7
%
$\frac{1}{8}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmfforce{1/2w,0h}{v7}
\fmfforce{1/2w,1h}{v8}
\fmf{boson}{v7,v8}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=0.4}{v4,v8}
\fmf{fermion,right=0.4}{v8,v3}
\fmf{fermion,right=0.4}{v3,v7}
\fmf{fermion,right=0.4}{v7,v4}
\fmf{boson,left=1}{v5,v6,v5}
\fmfdot{v7,v8,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #8
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{4/8w,1/2h}{v2}
\fmfforce{8/8w,1/2h}{v3}
\fmfforce{6/8w,2/8h}{v4}
\fmfforce{6/8w,6/8h}{v5}
\fmfforce{2/8w,2/8h}{v6}
\fmfforce{2/8w,6/8h}{v7}
\fmf{boson,right=1}{v6,v7,v6}
\fmf{fermion,right=0.5}{v5,v2}
\fmf{fermion,right=0.5}{v2,v4}
\fmf{fermion,right=0.5}{v4,v3}
\fmf{fermion,right=0.5}{v3,v5}
\fmf{boson,left=0.3}{v4,v3}
\fmf{boson,right=0.3}{v5,v3}
\fmfdot{v2,v3,v4,v5}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4022b}
%
% #9
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{4/8w,1/2h}{v2}
\fmfforce{8/8w,1/2h}{v3}
\fmfforce{6/8w,2/8h}{v4}
\fmfforce{6/8w,6/8h}{v5}
\fmfforce{2/8w,2/8h}{v6}
\fmfforce{2/8w,6/8h}{v7}
\fmf{boson,right=1}{v6,v7,v6}
\fmf{fermion,right=0.5}{v5,v2}
\fmf{fermion,right=0.5}{v2,v4}
\fmf{fermion,right=0.5}{v4,v3}
\fmf{fermion,right=0.5}{v3,v5}
\fmf{boson}{v4,v5}
\fmf{boson}{v4,v3}
\fmfdot{v2,v3,v4,v5}
\end{fmfgraph}
\end{center}}
%
% #10
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{4/8w,1/2h}{v2}
\fmfforce{8/8w,1/2h}{v3}
\fmfforce{6/8w,2/8h}{v4}
\fmfforce{6/8w,6/8h}{v5}
\fmfforce{2/8w,2/8h}{v6}
\fmfforce{2/8w,6/8h}{v7}
\fmf{boson,right=1}{v5,v4,v5}
\fmf{fermion,right=0.5}{v7,v1}
\fmf{fermion,right=0.5}{v1,v6}
\fmf{fermion,right=0.5}{v6,v2}
\fmf{fermion,right=0.5}{v2,v7}
\fmf{boson}{v6,v7}
\fmf{boson}{v6,v1}
\fmfdot{v2,v1,v6,v7}
\end{fmfgraph}
\end{center}}
%
% #11
%
${\displaystyle \frac{1}{2}}$
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(14,4)
\setval
\fmfforce{2/14w,0h}{v1}
\fmfforce{2/14w,1h}{v2}
\fmfforce{4/14w,1/2h}{v3}
\fmfforce{6/14w,0h}{v4}
\fmfforce{6/14w,1h}{v5}
\fmfforce{10/14w,1/2h}{v6}
\fmfforce{12/14w,0h}{v7}
\fmfforce{12/14w,1h}{v8}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=0.5}{v5,v3}
\fmf{fermion,right=0.5}{v3,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmf{boson,right=0.5}{v4,v6}
\fmf{boson,left=0.5}{v5,v6}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #12
%
$1$
%
\parbox{13mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{2/10w,0h}{v2}
\fmfforce{2/10w,1h}{v3}
\fmfforce{6/10w,1/2h}{v4}
\fmfforce{8/10w,1h}{v5}
\fmfforce{8/10w,0h}{v6}
\fmf{plain,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{fermion,right=0.4}{v1,v2}
\fmf{fermion,right=1}{v2,v3}
\fmf{boson,left=0.4}{v1,v2}
\fmf{boson,right=0.6}{v2,v4}
\fmf{boson,left=0.6}{v3,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #13
%
$1$
%
\parbox{13mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{2/10w,0h}{v1}
\fmfforce{2/10w,1h}{v2}
\fmfforce{4/10w,1/2h}{v3}
\fmfforce{8/10w,0h}{v4}
\fmfforce{8/10w,1h}{v5}
\fmfforce{10/10w,1/2h}{v6}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{boson,left=0.4}{v4,v6}
\fmf{fermion,right=0.4}{v4,v6}
\fmf{fermion,right=0.4}{v6,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{boson,right=0.6}{v3,v4}
\fmf{boson,left=0.6}{v3,v5}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #14
%
${\displaystyle \frac{1}{2}}$
%
\parbox{13mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{2/10w,0h}{v1}
\fmfforce{2/10w,1h}{v2}
\fmfforce{8/10w,0h}{v3}
\fmfforce{8/10w,1h}{v4}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{boson}{v1,v3}
\fmf{boson}{v2,v4}
\fmf{boson}{v3,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #15
%
${\displaystyle \frac{1}{2}}$
%
\parbox{12mm}{\begin{center}
\begin{fmfgraph}(10,4)
\setval
\fmfforce{2/10w,0h}{v1}
\fmfforce{2/10w,1h}{v2}
\fmfforce{5/10w,1/2h}{v3}
\fmfforce{8/10w,0h}{v4}
\fmfforce{8/10w,1h}{v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{boson,left=0.6}{v2,v5}
\fmf{boson,left=0.6}{v4,v1}
\fmf{boson,right=0.4}{v1,v3}
\fmf{boson,left=0.4}{v3,v5}
\fmfdot{v1,v2,v4,v5}
\end{fmfgraph}
\end{center}}
%
% #16
%
$1$
%
\parbox{7mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,0h}{v1}
\fmfforce{0w,1h}{v2}
\fmfforce{1w,1h}{v3}
\fmfforce{1w,0h}{v4}
\fmf{fermion,right=0.4}{v2,v1}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=0.4}{v4,v3}
\fmf{fermion,right=0.4}{v1,v4}
\fmf{boson,left=0.4}{v3,v2}
\fmf{boson,left=0.4}{v4,v3}
\fmf{boson,left=0.4}{v2,v1}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4022c}
%
% #17
%
${\displaystyle \frac{1}{2}}$
%
\parbox{7mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,0h}{v1}
\fmfforce{0w,1h}{v2}
\fmfforce{1w,1h}{v3}
\fmfforce{1w,0h}{v4}
\fmf{fermion,right=0.4}{v2,v1}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=0.4}{v4,v3}
\fmf{fermion,right=0.4}{v1,v4}
\fmf{boson}{v1,v3}
\fmf{boson}{v2,v4}
\fmf{boson}{v3,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #18
%
${\displaystyle \frac{1}{2}}$
%
\parbox{7mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,0h}{v1}
\fmfforce{0w,1h}{v2}
\fmfforce{1w,1h}{v3}
\fmfforce{1w,0h}{v4}
\fmf{fermion,right=0.4}{v2,v1}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=0.4}{v4,v3}
\fmf{fermion,right=0.4}{v1,v4}
\fmf{boson}{v1,v3}
\fmf{boson}{v2,v4}
\fmf{boson}{v1,v2}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #19
%
${\displaystyle \frac{1}{2}}$
%
\parbox{7mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,0h}{v1}
\fmfforce{0w,1h}{v2}
\fmfforce{1w,1h}{v3}
\fmfforce{1w,0h}{v4}
\fmf{fermion,right=0.4}{v2,v1}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=0.4}{v4,v3}
\fmf{fermion,right=0.4}{v1,v4}
\fmf{boson,right=0.4}{v2,v3}
\fmf{boson,left=0.4}{v1,v4}
\fmf{boson}{v2,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #20
%
${\displaystyle \frac{1}{2}}$
%
\parbox{7mm}{\begin{center}
\begin{fmfgraph}(4,4)
\setval
\fmfforce{0w,0h}{v1}
\fmfforce{0w,1h}{v2}
\fmfforce{1w,1h}{v3}
\fmfforce{1w,0h}{v4}
\fmf{fermion,right=0.4}{v2,v1}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=0.4}{v4,v3}
\fmf{fermion,right=0.4}{v1,v4}
\fmf{boson,right=0.4}{v1,v2}
\fmf{boson,right=0.4}{v3,v4}
\fmf{boson}{v2,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #21
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,8)
\setval
\fmfforce{2/12w,0h}{v1}
\fmfforce{2/12w,1/2h}{v2}
\fmfforce{4/12w,1/4h}{v3}
\fmfforce{8/12w,1/4h}{v4}
\fmfforce{10/12w,0h}{v5}
\fmfforce{10/12w,1/2h}{v6}
\fmfforce{4/12w,3/4h}{v7}
\fmfforce{8/12w,3/4h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,right=1}{v6,v5}
\fmf{fermion,right=1}{v7,v8}
\fmf{fermion,right=1}{v8,v7}
\fmf{boson}{v3,v4}
\fmf{boson}{v7,v3}
\fmf{boson}{v8,v4}
\fmfdot{v3,v4,v7,v8}
\end{fmfgraph}
\end{center}}
%
% #22
%
${\displaystyle \frac{1}{4}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,12)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1/3h}{v2}
\fmfforce{1/3w,1/6h}{v3}
\fmfforce{2/3w,1/6h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1/3h}{v6}
\fmfforce{1/2w,1/3h}{v7}
\fmfforce{1/3w,5/6h}{v8}
\fmfforce{2/3w,5/6h}{v9}
\fmfforce{1/2w,2/3h}{v10}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson,left=1}{v5,v6,v5}
\fmf{boson}{v7,v10}
\fmf{fermion,right=1}{v9,v8}
\fmf{fermion,right=1}{v8,v9}
\fmfdot{v3,v4,v7,v10}
\end{fmfgraph}
\end{center}} 
%
% #23
%
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,1h}{v2}
\fmfforce{4/16w,1/2h}{v3}
\fmfforce{8/16w,1/2h}{v4}
\fmfforce{12/16w,1/2h}{v5}
\fmfforce{1w,1/2h}{v6}
\fmf{boson}{v4,v6}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #24
%
$\frac{1}{8}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,0h}{v1}
\fmfforce{1/10w,1h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v4}
\fmfforce{3/5w,1/2h}{v5}
\fmfforce{4/5w,1/2h}{v6}
\fmfforce{9/10w,0h}{v7}
\fmfforce{9/10w,1h}{v8}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{boson}{v4,v5}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{boson,right=1}{v8,v7,v8}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4022d}
%
% #25
%
${\displaystyle \frac{1}{2}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,0h}{v1}
\fmfforce{1/10w,1h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v4}
\fmfforce{3/5w,1/2h}{v5}
\fmfforce{4/5w,1/2h}{v6}
\fmfforce{9/10w,0h}{v7}
\fmfforce{9/10w,1h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v3,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{boson,right=1}{v5,v6,v5}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #26
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,14)
\setval
\fmfforce{0w,3/14h}{v1}
\fmfforce{1w,3/14h}{v2}
\fmfforce{1/6w,12/14h}{v3}
\fmfforce{5/6w,12/14h}{v4}
\fmfforce{0.5w,6/14h}{v5}
\fmfforce{0.5w,10/14h}{v6}
\fmf{fermion,right=0.4}{v2,v5}
\fmf{fermion,right=0.4}{v5,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{boson,right=0.4}{v1,v2,v1}
\fmf{fermion,right=1}{v4,v3}
\fmf{plain,right=1}{v3,v4}
\fmf{boson}{v5,v6}
\fmfdot{v1,v2,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #27
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,12)
\setval
\fmfforce{2/8w,0h}{v1}
\fmfforce{2/8w,1/3h}{v2}
\fmfforce{4/8w,1/6h}{v3}
\fmfforce{6/8w,0h}{v4}
\fmfforce{6/8w,1/3h}{v5}
\fmfforce{6/8w,2/3h}{v6}
\fmfforce{4/8w,5/6h}{v7}
\fmfforce{8/8w,5/6h}{v8}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{fermion,right=0.5}{v5,v3}
\fmf{fermion,right=0.5}{v3,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{boson}{v4,v6}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}
\end{center}} 
%
% #28
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,12)
\setval
\fmfforce{6/8w,0h}{v1}
\fmfforce{6/8w,1/3h}{v2}
\fmfforce{4/8w,1/6h}{v3}
\fmfforce{2/8w,0h}{v4}
\fmfforce{2/8w,1/3h}{v5}
\fmfforce{2/8w,2/3h}{v6}
\fmfforce{0/8w,5/6h}{v7}
\fmfforce{4/8w,5/6h}{v8}
\fmfforce{0w,1/6h}{v9}
\fmf{boson,left=1}{v1,v2,v1}
\fmf{fermion,right=0.5}{v3,v5}
\fmf{fermion,right=0.5}{v4,v3}
\fmf{fermion,right=1}{v5,v4}
\fmf{boson}{v4,v6}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}
\end{center}} 
%
% #29
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,10)
\setval
\fmfforce{0/12w,2/10h}{v1}
\fmfforce{4/12w,2/10h}{v2}
\fmfforce{8/12w,2/10h}{v3}
\fmfforce{10/12w,0h}{v4}
\fmfforce{10/12w,4/10h}{v5}
\fmfforce{2/12w,6/10h}{v6}
\fmfforce{0/12w,8/10h}{v7}
\fmfforce{4/12w,8/10h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{plain,right=1}{v5,v4}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmf{boson}{v2,v3}
\fmf{boson,right=0.6}{v6,v1}
\fmf{boson,right=0.6}{v2,v6}
\fmfdot{v1,v2,v3,v6}
\end{fmfgraph}
\end{center}}
%
% #30
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(14,6)
\setval
\fmfforce{3/14w,0h}{v1}
\fmfforce{3/14w,1h}{v2}
\fmfforce{6/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4}
\fmfforce{12/14w,1/6h}{v5}
\fmfforce{12/14w,5/6h}{v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,right=1}{v6,v5}
\fmf{boson}{v1,v2}
\fmf{boson,right=0.4}{v2,v3}
\fmf{boson}{v3,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #31
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(14,6)
\setval
\fmfforce{3/14w,0h}{v1}
\fmfforce{3/14w,1h}{v2}
\fmfforce{6/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4}
\fmfforce{12/14w,1/6h}{v5}
\fmfforce{12/14w,5/6h}{v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,right=1}{v6,v5}
\fmf{boson}{v1,v2}
\fmf{boson,right=0.4}{v3,v1}
\fmf{boson}{v3,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4022e}
%
% #32
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{0/12w,1/2h}{v1}
\fmfforce{4/12w,1/2h}{v2}
\fmfforce{8/12w,1/2h}{v3}
\fmfforce{12/12w,1/2h}{v4}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{boson}{v1,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #33
%
$1$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,6)
\setval
\fmfforce{0/16w,1/3h}{v1}
\fmfforce{4/16w,1/3h}{v2}
\fmfforce{8/16w,1/3h}{v3}
\fmfforce{6/16w,2/3h}{v4}
\fmfforce{10/16w,2/3h}{v5}
\fmfforce{12/16w,1/3h}{v6}
\fmfforce{14/16w,0h}{v7}
\fmfforce{14/16w,2/3h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v5,v4}
\fmf{plain,right=1}{v4,v5}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmf{boson}{v1,v6}
\fmfdot{v1,v2,v3,v6}
\end{fmfgraph}
\end{center}}
%
% #34
%
${\displaystyle \frac{1}{2}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{2/20w,0h}{v1}
\fmfforce{2/20w,1h}{v2}
\fmfforce{4/20w,1/2h}{v3}
\fmfforce{8/20w,1/2h}{v4}
\fmfforce{12/20w,1/2h}{v5}
\fmfforce{16/20w,1/2h}{v6}
\fmfforce{18/20w,0h}{v7}
\fmfforce{18/20w,1h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmf{boson}{v3,v6}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #35
%
${\displaystyle \frac{1}{2}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,6)
\setval
\fmfforce{2/20w,0h}{v1}
\fmfforce{2/20w,2/3h}{v2}
\fmfforce{4/20w,1/3h}{v3}
\fmfforce{8/20w,1/3h}{v4}
\fmfforce{12/20w,1/3h}{v5}
\fmfforce{16/20w,1/3h}{v6}
\fmfforce{18/20w,0h}{v7}
\fmfforce{18/20w,2/3h}{v8}
\fmfforce{10/20w,2/3h}{v9}
\fmfforce{14/20w,2/3h}{v10}
\fmf{boson}{v4,v6}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmf{fermion,right=1}{v10,v9}
\fmf{plain,right=1}{v9,v10}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #36
%
${\displaystyle \frac{1}{4}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(16,10)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,4/10h}{v2}
\fmfforce{4/16w,2/10h}{v3}
\fmfforce{8/16w,2/10h}{v4}
\fmfforce{12/16w,2/10h}{v5}
\fmfforce{14/16w,0h}{v6}
\fmfforce{14/16w,4/10h}{v7}
\fmfforce{1/2w,6/10h}{v8}
\fmfforce{6/16w,8/10h}{v9}
\fmfforce{10/16w,8/10h}{v10}
\fmf{boson}{v3,v4}
\fmf{boson}{v4,v5}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,left=1}{v6,v7}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v4,v8}
\fmf{fermion,right=1}{v8,v4}
\fmf{boson,right=1}{v9,v10}
\fmf{boson,right=1}{v10,v9}
\fmfdot{v3,v4,v5,v8}
\end{fmfgraph}\end{center}} 
%
% #37
%
${\displaystyle \frac{1}{2}}$
%
\parbox{25mm}{\begin{center}
\begin{fmfgraph}(22,6)
\setval
\fmfforce{2/22w,0h}{v1}
\fmfforce{2/22w,2/3h}{v2}
\fmfforce{8/22w,1/3h}{v3}
\fmfforce{8/22w,1h}{v4}
\fmfforce{14/22w,1/3h}{v5}
\fmfforce{12/22w,1h}{v6}
\fmfforce{18/22w,1/3h}{v7}
\fmfforce{20/22w,0h}{v8}
\fmfforce{20/22w,2/3h}{v9}
\fmfforce{4/22w,1/3h}{v10}
\fmfforce{6/22w,2/3h}{v11}
\fmfforce{10/22w,2/3h}{v12}
\fmfforce{12/22w,2/3h}{v13}
\fmfforce{16/22w,2/3h}{v14}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v12,v11}
\fmf{plain,right=1}{v11,v12}
\fmf{fermion,right=1}{v14,v13}
\fmf{plain,right=1}{v13,v14}
\fmf{fermion,right=1}{v8,v9}
\fmf{plain,right=1}{v9,v8}
\fmf{boson}{v10,v7}
\fmfdot{v3,v5,v7,v10}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\
%
$4$ & $0$ & $3$ & $0$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4030a}
%
% #1
%
${\displaystyle \frac{1}{4}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/4w,1/2h}{v2}
\fmfforce{2/4w,1/2h}{v3}
\fmfforce{3/4w,1/2h}{v4}
\fmfforce{4/4w,1/2h}{v5}
\fmfforce{7/8w,0h}{v6}
\fmfforce{7/8w,1h}{v7}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{boson,right=1}{v3,v4,v3}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v3,v2}
\fmf{plain,left=1}{v6,v7}
\fmf{fermion,right=1}{v6,v7}
\fmfdot{v2,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #2
%
$\frac{1}{24}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,8)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1/2h}{v2}
\fmfforce{1/3w,1/4h}{v3}
\fmfforce{2/3w,1/4h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1/2h}{v6}
\fmfforce{1/2w,1/2h}{v7}
\fmfforce{1/2w,1h}{v8}
\fmfforce{1w,1/4h}{v9}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson,right=1}{v4,v9,v4}
\fmf{boson,right=1}{v7,v8,v7}
\fmfdot{v3,v4,v7}
\end{fmfgraph}
\end{center}} 
%
% #3
%
$\frac{1}{24}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,8)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1/2h}{v2}
\fmfforce{1/3w,1/4h}{v3}
\fmfforce{2/3w,1/4h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1/2h}{v6}
\fmfforce{1/2w,1/2h}{v7}
\fmfforce{1/2w,1h}{v8}
\fmfforce{1w,1/4h}{v9}
\fmfforce{1/3w,3/4h}{v10}
\fmfforce{2/3w,3/4h}{v11}
\fmf{plain,left=1}{v2,v1}
\fmf{fermion,right=1}{v2,v1}
\fmf{boson,right=1}{v3,v4,v3}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,right=1}{v10,v11}
\fmf{fermion,right=1}{v11,v10}
\fmfdot{v3,v4,v7}
\end{fmfgraph}
\end{center}} 
%
% #4
%
${\displaystyle \frac{1}{4}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{0w,0.3h}{v1}
\fmfforce{1w,0.3h}{v2}
\fmfforce{1/6w,0.8h}{v3}
\fmfforce{5/6w,0.8h}{v4}
\fmfforce{0.5w,0.6h}{v5}
\fmf{fermion,right=0.4}{v2,v5}
\fmf{fermion,right=0.4}{v5,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{boson,right=0.4}{v1,v2}
\fmf{boson,right=0.4}{v2,v1}
\fmf{boson,right=1}{v4,v3,v4}
\fmfdot{v1,v2,v5}
\end{fmfgraph}\end{center}} 
%
% #5
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{0w,0.3h}{v1}
\fmfforce{1w,0.3h}{v2}
\fmfforce{1/6w,0.8h}{v3}
\fmfforce{5/6w,0.8h}{v4}
\fmfforce{0.5w,0.6h}{v5}
\fmf{boson,right=0.4}{v2,v5}
\fmf{boson,right=0.4}{v5,v1}
\fmf{boson,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v1,v2}
\fmf{fermion,right=0.4}{v2,v1}
\fmf{fermion,right=1}{v4,v3}
\fmf{plain,right=1}{v3,v4}
\fmfdot{v1,v2,v5}
\end{fmfgraph}\end{center}} 
%
% #6
%
$\frac{1}{3}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,6)
\setval
\fmfforce{0.5w,1h}{v1}
\fmfforce{0.066987w,0.25h}{v2}
\fmfforce{0.93301w,0.25h}{v3}
\fmf{fermion,right=0.5}{v1,v2}
\fmf{fermion,right=0.5}{v2,v3}
\fmf{fermion,right=0.5}{v3,v1}
\fmf{boson}{v1,v3}
\fmf{boson}{v3,v2}
\fmf{boson}{v2,v1}
\fmfdot{v2,v3,v1}
\end{fmfgraph}
\end{center}} 
%
\end{fmffile}
%
\\
%
$4$ & $1$ & $0$ & $4$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4104a}
%
% #1
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{2/8w,0h}{v1}
\fmfforce{2/8w,1h}{v2}
\fmfforce{1/2w,1/2h}{v3}
\fmfforce{6/8w,0h}{v4}
\fmfforce{6/8w,1h}{v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=0.5}{v3,v2}
\fmf{fermion,right=0.5}{v1,v3}
\fmf{fermion,right=0.5}{v5,v3}
\fmf{fermion,right=0.5}{v3,v4}
\fmf{boson}{v1,v2}
\fmf{boson}{v4,v5}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #2
%
$1$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{1/2w,0h}{v1}
\fmfforce{1/2w,6/10h}{v2}
\fmfforce{1/6w,8/10h}{v3}
\fmfforce{5/6w,8/10h}{v4}
\fmfforce{0.9/6w,1/10h}{v5}
\fmfforce{0.9/6w,5/10h}{v6}
\fmfforce{5.1/6w,1/10h}{v7}
\fmfforce{5.1/6w,5/10h}{v8}
\fmf{fermion,right=0.2}{v8,v2}
\fmf{fermion,right=0.2}{v2,v6}
\fmf{fermion,right=0.45}{v6,v5}
\fmf{fermion,right=0.45}{v5,v7}
\fmf{fermion,right=0.45}{v7,v8}
\fmf{fermion,right=1}{v4,v3}
\fmf{plain,left=1}{v4,v3}
\fmf{boson,left=0.45}{v7,v8}
\fmf{boson,right=0.45}{v5,v6}
\fmfdot{v2,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #3
%
$1$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{1/2w,0h}{v1}
\fmfforce{1/2w,6/10h}{v2}
\fmfforce{1/6w,8/10h}{v3}
\fmfforce{5/6w,8/10h}{v4}
\fmfforce{0.9/6w,1/10h}{v5}
\fmfforce{0.9/6w,5/10h}{v6}
\fmfforce{5.1/6w,1/10h}{v7}
\fmfforce{5.1/6w,5/10h}{v8}
\fmf{fermion,right=0.2}{v8,v2}
\fmf{fermion,right=0.2}{v2,v6}
\fmf{fermion,right=0.45}{v6,v5}
\fmf{fermion,right=0.45}{v5,v7}
\fmf{fermion,right=0.45}{v7,v8}
\fmf{fermion,right=1}{v4,v3}
\fmf{plain,left=1}{v4,v3}
\fmf{boson,right=0.45}{v7,v5}
\fmf{boson,left=0.45}{v8,v6}
\fmfdot{v2,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #4
%
$1$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{1/2w,0h}{v1}
\fmfforce{1/2w,6/10h}{v2}
\fmfforce{1/6w,8/10h}{v3}
\fmfforce{5/6w,8/10h}{v4}
\fmfforce{0.9/6w,1/10h}{v5}
\fmfforce{0.9/6w,5/10h}{v6}
\fmfforce{5.1/6w,1/10h}{v7}
\fmfforce{5.1/6w,5/10h}{v8}
\fmf{fermion,right=0.2}{v8,v2}
\fmf{fermion,right=0.2}{v2,v6}
\fmf{fermion,right=0.45}{v6,v5}
\fmf{fermion,right=0.45}{v5,v7}
\fmf{fermion,right=0.45}{v7,v8}
\fmf{fermion,right=1}{v4,v3}
\fmf{plain,left=1}{v4,v3}
\fmf{boson}{v7,v6}
\fmf{boson}{v8,v5}
\fmfdot{v2,v5,v6,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #5
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{2/8w,0h}{v1}
\fmfforce{2/8w,1h}{v2}
\fmfforce{4/8w,1/2h}{v3}
\fmfforce{6/8w,0h}{v4}
\fmfforce{6/8w,1h}{v5}
\fmfforce{1w,1/2h}{v6}
\fmf{fermion,right=0.4}{v6,v5}
\fmf{fermion,right=0.4}{v5,v3}
\fmf{fermion,right=0.4}{v3,v4}
\fmf{fermion,right=0.4}{v4,v6}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=0.4}{v1,v3}
\fmf{boson,left=0.6}{v2,v5}
\fmf{boson,left=0.4}{v4,v6}
\fmfdot{v2,v3,v4,v5,v6}
\end{fmfgraph}
\end{center}} 
%
% #6
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,4)
\setval
\fmfforce{2/8w,0h}{v1}
\fmfforce{2/8w,1h}{v2}
\fmfforce{4/8w,1/2h}{v3}
\fmfforce{6/8w,0h}{v4}
\fmfforce{6/8w,1h}{v5}
\fmfforce{0w,1/2h}{v6}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=0.4}{v5,v3}
\fmf{plain,right=0.4}{v3,v4}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=0.4}{v2,v6}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{boson,left=0.6}{v2,v5}
\fmf{fermion,right=0.4}{v6,v1}
\fmf{boson,right=0.4}{v1,v6}
\fmfdot{v1,v2,v3,v6,v5}
\end{fmfgraph}
\end{center}} 
%
% #7
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,6)
\setval
\fmfforce{0/8w,1/3h}{v1}
\fmfforce{4/8w,1/3h}{v2}
\fmfforce{6/8w,0h}{v3}
\fmfforce{6/8w,2/3h}{v4}
\fmfforce{8/8w,1/3h}{v5}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v4,v2}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=0.4}{v3,v5}
\fmf{fermion,right=0.4}{v5,v4}
\fmf{boson}{v3,v4}
\fmf{boson,right=1}{v5,v1}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #8
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{2/8w,1/4h}{v1}
\fmfforce{2/8w,3/4h}{v2}
\fmfforce{4/8w,1/2h}{v3}
\fmfforce{6/8w,1/4h}{v4}
\fmfforce{6/8w,3/4h}{v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=0.4}{v5,v3}
\fmf{fermion,right=0.4}{v3,v4}
\fmf{boson,left=0.6}{v2,v5}
\fmf{boson,left=0.6}{v4,v1}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4104b}
%
% #9
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,6)
\setval
\fmfforce{0/8w,1/3h}{v1}
\fmfforce{2/8w,2/3h}{v2}
\fmfforce{4/8w,1/3h}{v3}
\fmfforce{6/8w,2/3h}{v4}
\fmfforce{8/8w,1/3h}{v5}
\fmf{fermion,right=1}{v1,v3}
\fmf{fermion,right=1}{v3,v5}
\fmf{fermion,right=0.4}{v2,v1}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=0.4}{v4,v3}
\fmf{fermion,right=0.4}{v5,v4}
\fmf{boson,left=1}{v1,v4}
\fmf{boson,left=1}{v2,v5}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #10
%
$1$
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(14,4)
\setval
\fmfforce{2/14w,0h}{v1}
\fmfforce{2/14w,1h}{v2}
\fmfforce{4/14w,1/2h}{v3}
\fmfforce{6/14w,0h}{v4}
\fmfforce{6/14w,1h}{v5}
\fmfforce{12/14w,0h}{v6}
\fmfforce{12/14w,1h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v5,v3}
\fmf{fermion,right=0.4}{v3,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\fmf{boson}{v6,v4}
\fmf{boson}{v7,v5}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #11
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,10)
\setval
\fmfforce{2/8w,4/10h}{v1}
\fmfforce{2/8w,8/10h}{v2}
\fmfforce{4/8w,2/10h}{v3}
\fmfforce{6/8w,4/10h}{v4}
\fmfforce{6/8w,8/10h}{v5}
\fmfforce{2/8w,0h}{v6}
\fmfforce{6/8w,0h}{v7}
\fmf{fermion,right=1}{v2,v5}
\fmf{fermion,right=1}{v5,v2}
\fmf{fermion,right=1}{v1,v6}
\fmf{plain,right=1}{v6,v1}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{fermion,right=1}{v7,v4}
\fmf{plain,left=1}{v7,v4}
\fmf{fermion,right=0.4}{v4,v3}
\fmf{boson}{v1,v2}
\fmf{boson}{v4,v5}
\fmfdot{v1,v2,v3,v4,v5}
\end{fmfgraph}
\end{center}} 
%
% #12
%
$1$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,1h}{v2}
\fmfforce{4/16w,1/2h}{v3}
\fmfforce{8/16w,1/2h}{v4}
\fmfforce{12/16w,1/2h}{v5}
\fmfforce{14/16w,0h}{v6}
\fmfforce{14/16w,1h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v4,v5}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=0.5}{v5,v6}
\fmf{fermion,right=0.5}{v7,v5}
\fmf{boson}{v6,v7}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #13
%
$1$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,1h}{v2}
\fmfforce{4/16w,1/2h}{v3}
\fmfforce{8/16w,1/2h}{v4}
\fmfforce{12/16w,1/2h}{v5}
\fmfforce{14/16w,0h}{v6}
\fmfforce{14/16w,1h}{v7}
\fmfforce{6/16w,0h}{v8}
\fmfforce{6/16w,1h}{v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v8,v9}
\fmf{fermion,right=1}{v6,v7}
\fmf{plain,right=1}{v7,v6}
\fmf{fermion,right=0.5}{v9,v3}
\fmf{fermion,right=0.5}{v3,v8}
\fmf{fermion,right=0.5}{v8,v4}
\fmf{fermion,right=0.5}{v4,v9}
\fmf{boson}{v4,v5}
\fmfdot{v3,v4,v5,v8,v9}
\end{fmfgraph}
\end{center}} 
%
% #14
%
$1$
%
\parbox{27mm}{\begin{center}
\begin{fmfgraph}(24,4)
\setval
\fmfforce{2/24w,0h}{v1}
\fmfforce{2/24w,1h}{v2}
\fmfforce{4/24w,1/2h}{v3}
\fmfforce{8/24w,1/2h}{v4}
\fmfforce{12/24w,1/2h}{v5}
\fmfforce{16/24w,1/2h}{v6}
\fmfforce{20/24w,1/2h}{v7}
\fmfforce{22/24w,0h}{v8}
\fmfforce{22/24w,1h}{v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v4,v5}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{fermion,right=1}{v8,v9}
\fmf{plain,right=1}{v9,v8}
\fmf{boson}{v6,v7}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4104c}
%
% #15
%
$1$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,1h}{v2}
\fmfforce{4/16w,1/2h}{v3}
\fmfforce{8/16w,1/2h}{v4}
\fmfforce{12/16w,1/2h}{v5}
\fmfforce{14/16w,0h}{v6}
\fmfforce{14/16w,1h}{v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v3,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=0.5}{v5,v6}
\fmf{fermion,right=0.5}{v7,v5}
\fmf{boson}{v6,v7}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #16
%
$1$
%
\parbox{21mm}{\begin{center}
\begin{fmfgraph}(18,6)
\setval
\fmfforce{2/18w,1/6h}{v1}
\fmfforce{2/18w,5/6h}{v2}
\fmfforce{4/18w,1/2h}{v3}
\fmfforce{10/18w,1/2h}{v4}
\fmfforce{14/18w,1/2h}{v5}
\fmfforce{16/18w,1/6h}{v6a}
\fmfforce{16/18w,5/6h}{v6b}
\fmfforce{5/18w,0.9h}{v7}
\fmfforce{9/18w,0.9h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.32}{v4,v8}
\fmf{fermion,right=0.32}{v8,v7}
\fmf{boson,left=0.4}{v8,v7}
\fmf{fermion,right=0.25}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{plain,left=1}{v6a,v6b}
\fmf{fermion,right=1}{v6a,v6b}
\fmf{boson}{v4,v5}
\fmfdot{v3,v4,v7,v8,v5}
\end{fmfgraph}
\end{center}} 
%
% #17
%
$1$
%
\parbox{21mm}{\begin{center}
\begin{fmfgraph}(18,6)
\setval
\fmfforce{2/18w,1/6h}{v1}
\fmfforce{2/18w,5/6h}{v2}
\fmfforce{4/18w,1/2h}{v3}
\fmfforce{8/18w,1/2h}{v4}
\fmfforce{14/18w,1/2h}{v5}
\fmfforce{16/18w,1/6h}{v6a}
\fmfforce{16/18w,5/6h}{v6b}
\fmfforce{9/18w,0.9h}{v7}
\fmfforce{13/18w,0.9h}{v8}
\fmf{boson}{v3,v4}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.32}{v5,v8}
\fmf{fermion,right=0.32}{v8,v7}
\fmf{boson,left=0.4}{v8,v7}
\fmf{fermion,right=0.25}{v7,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{plain,left=1}{v6a,v6b}
\fmf{fermion,right=1}{v6a,v6b}
\fmfdot{v3,v4,v7,v8,v5}
\end{fmfgraph}
\end{center}} 
%
% #18
%
$1$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,1h}{v2}
\fmfforce{4/16w,1/2h}{v3}
\fmfforce{8/16w,1/2h}{v4}
\fmfforce{10/16w,0h}{v5}
\fmfforce{10/16w,1h}{v6}
\fmfforce{6/16w,1h}{v7}
\fmfforce{12/16w,1/2h}{v8}
\fmfforce{14/16w,0h}{v9}
\fmfforce{14/16w,1h}{v10}
\fmf{boson,left=0.6}{v2,v7}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson}{v4,v8}
\fmf{plain,left=1}{v9,v10}
\fmf{fermion,right=1}{v9,v10}
\fmfdot{v2,v7,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #19
%
$1$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,1h}{v2}
\fmfforce{4/16w,1/2h}{v3}
\fmfforce{8/16w,1/2h}{v4}
\fmfforce{10/16w,0h}{v5}
\fmfforce{10/16w,1h}{v6}
\fmfforce{12/16w,1/2h}{v7}
\fmfforce{14/16w,0h}{v8}
\fmfforce{14/16w,1h}{v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v3,v4}
\fmf{boson,left=0.6}{v6,v9}
\fmf{fermion,right=1}{v8,v9}
\fmf{fermion,right=0.4}{v7,v6}
\fmf{plain,left=1}{v8,v9}
\fmf{plain,right=0.4}{v7,v8}
\fmf{fermion,right=0.4}{v9,v7}
\fmf{fermion,right=1}{v4,v7}
\fmf{fermion,right=0.4}{v6,v4}
\fmfdot{v3,v4,v6,v9,v7}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4104d}
%
% #20
%
${\displaystyle \frac{1}{2}}$
%
\parbox{27mm}{\begin{center}
\begin{fmfgraph}(24,4)
\setval
\fmfforce{2/24w,0h}{v1}
\fmfforce{2/24w,1h}{v2}
\fmfforce{4/24w,1/2h}{v3}
\fmfforce{8/24w,1/2h}{v4}
\fmfforce{12/24w,1/2h}{v5}
\fmfforce{16/24w,1/2h}{v6}
\fmfforce{20/24w,1/2h}{v7}
\fmfforce{22/24w,0h}{v8}
\fmfforce{22/24w,1h}{v9}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{fermion,right=1}{v8,v9}
\fmf{plain,right=1}{v9,v8}
\fmf{boson}{v6,v7}
\fmf{boson}{v3,v4}
\fmfdot{v3,v4,v5,v6,v7}
\end{fmfgraph}
\end{center}} 
%
% #21
%
$1$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,8)
\setval
\fmfforce{2/20w,0h}{v1}
\fmfforce{2/20w,1/2h}{v2}
\fmfforce{4/20w,1/4h}{v3}
\fmfforce{8/20w,1/4h}{v4}
\fmfforce{12/20w,1/4h}{v5}
\fmfforce{16/20w,1/4h}{v6}
\fmfforce{18/20w,0h}{v7}
\fmfforce{18/20w,1/2h}{v8}
\fmfforce{10/20w,1/2h}{v9}
\fmfforce{8/20w,6/8h}{v10}
\fmfforce{12/20w,6/8h}{v11}
\fmf{boson}{v3,v4}
\fmf{boson}{v5,v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,left=1}{v2,v1}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmf{fermion,right=1}{v11,v10}
\fmf{plain,right=1}{v10,v11}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=0.4}{v5,v9}
\fmf{fermion,right=0.4}{v9,v4}
\fmfdot{v3,v4,v5,v6,v9}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\
%
$4$ & $1$ & $1$ & $2$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4112a}
%
% #1
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmf{boson}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson,left=1}{v5,v6,v5}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #2
%
${\displaystyle \frac{1}{2}}$
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(14,4)
\setval
\fmfforce{2/14w,0h}{v1}
\fmfforce{2/14w,1h}{v2}
\fmfforce{4/14w,1/2h}{v3}
\fmfforce{8/14w,1/2h}{v4}
\fmfforce{10/14w,1/2h}{v5}
\fmfforce{12/14w,0h}{v6}
\fmfforce{12/14w,1h}{v7}
\fmfforce{12/14w,1/2h}{v8}
\fmfforce{1w,1/2h}{v9}
\fmfdot{v3,v4,v6,v7}
\fmf{plain,left}{v2,v1}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson,right=0.5}{v4,v6}
\fmf{boson,left=0.5}{v4,v7}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\end{fmfgraph}
\end{center}} 
%
% #3
%
${\displaystyle \frac{1}{2}}$
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(14,6)
\setval
\fmfforce{2/14w,1/6h}{v1}
\fmfforce{2/14w,5/6h}{v2}
\fmfforce{4/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4}
\fmfforce{12/14w,1/6h}{v5}
\fmfforce{12/14w,5/6h}{v6}
\fmfforce{5/14w,0.9h}{v7}
\fmfforce{9/14w,0.9h}{v8}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=0.32}{v4,v8}
\fmf{fermion,right=0.32}{v8,v7}
\fmf{boson,left=0.4}{v8,v7}
\fmf{fermion,right=0.25}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v3,v4,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #4
%
${\displaystyle \frac{1}{2}}$
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(14,6)
\setval
\fmfforce{2/14w,1/6h}{v1}
\fmfforce{2/14w,5/6h}{v2}
\fmfforce{4/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4}
\fmfforce{12/14w,1/6h}{v5}
\fmfforce{12/14w,5/6h}{v6}
\fmfforce{5/14w,0.9h}{v7}
\fmfforce{9/14w,0.9h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.32}{v4,v8}
\fmf{fermion,right=0.32}{v8,v7}
\fmf{boson,left=0.4}{v8,v7}
\fmf{fermion,right=0.25}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson,left=1}{v5,v6,v5}
\fmfdot{v3,v4,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #5
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmfforce{1/2w,0h}{v7}
\fmfforce{1/2w,1h}{v8}
\fmf{boson}{v7,v8}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=0.4}{v4,v8}
\fmf{fermion,right=0.4}{v8,v3}
\fmf{fermion,right=0.4}{v3,v7}
\fmf{fermion,right=0.4}{v7,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v7,v8,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #6
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmfforce{1/2w,1h}{v7}
\fmf{boson,left=0.6}{v2,v7}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson,left=1}{v5,v6,v5}
\fmfdot{v2,v7,v3,v4}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4112b}
%
% #7
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmfforce{1/2w,1h}{v7}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{boson,left=0.6}{v7,v6}
\fmf{boson,right=1}{v2,v1,v2}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v6,v7,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #8
%
$1$
%
\parbox{17mm}{\begin{center}
\begin{fmfgraph}(14,4)
\setval
\fmfforce{2/14w,0h}{v1}
\fmfforce{2/14w,1h}{v2}
\fmfforce{4/14w,1/2h}{v3}
\fmfforce{6/14w,0h}{v4}
\fmfforce{6/14w,1h}{v5}
\fmfforce{10/14w,1/2h}{v6}
\fmfforce{12/14w,0h}{v7}
\fmfforce{12/14w,1h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.5}{v5,v3}
\fmf{fermion,right=0.5}{v3,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmf{boson,right=0.5}{v4,v6}
\fmf{boson,left=0.5}{v5,v6}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #9
%
${\displaystyle \frac{1}{2}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,10)
\setval
\fmfforce{0w,2/10h}{v1}
\fmfforce{4/8w,2/10h}{v2}
\fmfforce{8/8w,2/10h}{v3}
\fmfforce{2/8w,4/10h}{v4}
\fmfforce{6/8w,4/10h}{v5}
\fmfforce{4/8w,6/10h}{v6}
\fmfforce{2/8w,8/10h}{v7}
\fmfforce{6/8w,8/10h}{v8}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=0.5}{v2,v4}
\fmf{plain,right=0.5}{v4,v1}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=0.5}{v5,v2}
\fmf{plain,right=0.5}{v3,v5}
\fmf{boson,left=1}{v4,v5}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,left=1}{v8,v7}
\fmfdot{v2,v4,v5,v6}
\end{fmfgraph}
\end{center}}
%
% #10
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{4/8w,1/2h}{v2}
\fmfforce{8/8w,1/2h}{v3}
\fmfforce{6/8w,2/8h}{v4}
\fmfforce{6/8w,6/8h}{v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=0.5}{v5,v2}
\fmf{fermion,right=0.5}{v2,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{boson,right=0.7}{v1,v4}
\fmf{boson,left=0.7}{v1,v5}
\fmfdot{v1,v2,v4,v5}
\end{fmfgraph}
\end{center}}
%
% #11
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{4/8w,1/2h}{v2}
\fmfforce{8/8w,1/2h}{v3}
\fmfforce{6/8w,2/8h}{v4}
\fmfforce{6/8w,6/8h}{v5}
\fmfforce{2/8w,2/8h}{v6}
\fmfforce{2/8w,6/8h}{v7}
\fmf{plain,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\fmf{fermion,right=0.5}{v5,v2}
\fmf{fermion,right=0.5}{v2,v4}
\fmf{fermion,right=0.5}{v4,v3}
\fmf{fermion,right=0.5}{v3,v5}
\fmf{boson,left=0.3}{v4,v3}
\fmf{boson,right=0.3}{v5,v3}
\fmfdot{v2,v3,v4,v5}
\end{fmfgraph}
\end{center}}
%
% #12
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{4/8w,1/2h}{v2}
\fmfforce{8/8w,1/2h}{v3}
\fmfforce{6/8w,2/8h}{v4}
\fmfforce{6/8w,6/8h}{v5}
\fmfforce{2/8w,2/8h}{v6}
\fmfforce{2/8w,6/8h}{v7}
\fmf{plain,right=1}{v6,v7}
\fmf{fermion,right=1}{v7,v6}
\fmf{fermion,right=0.5}{v5,v2}
\fmf{fermion,right=0.5}{v2,v4}
\fmf{fermion,right=0.5}{v4,v3}
\fmf{fermion,right=0.5}{v3,v5}
\fmf{boson}{v4,v5}
\fmf{boson}{v4,v3}
\fmfdot{v2,v3,v4,v5}
\end{fmfgraph}
\end{center}}
%
% #13
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{4/8w,1/2h}{v2}
\fmfforce{8/8w,1/2h}{v3}
\fmfforce{6/8w,2/8h}{v4}
\fmfforce{6/8w,6/8h}{v5}
\fmfforce{2/8w,2/8h}{v6}
\fmfforce{2/8w,6/8h}{v7}
\fmf{plain,right=1}{v5,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=0.5}{v7,v1}
\fmf{fermion,right=0.5}{v1,v6}
\fmf{fermion,right=0.5}{v6,v2}
\fmf{fermion,right=0.5}{v2,v7}
\fmf{boson}{v6,v7}
\fmf{boson}{v6,v1}
\fmfdot{v2,v1,v6,v7}
\end{fmfgraph}
\end{center}}
%
% #14
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,6)
\setval
\fmfforce{2/8w,0h}{v1}
\fmfforce{2/8w,2/3h}{v2}
\fmfforce{4/8w,1/3h}{v3}
\fmfforce{6/8w,0h}{v4}
\fmfforce{6/8w,2/3h}{v5}
\fmf{boson}{v1,v2}
\fmf{boson,left=1}{v2,v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.5}{v3,v2}
\fmf{fermion,right=0.5}{v1,v3}
\fmf{fermion,right=0.5}{v5,v3}
\fmf{fermion,right=1}{v4,v5}
\fmf{plain,right=0.5}{v3,v4}
\fmfdot{v1,v2,v3,v5}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4112c}
%
% #15
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,6)
\setval
\fmfforce{2/8w,0h}{v1}
\fmfforce{2/8w,2/3h}{v2}
\fmfforce{4/8w,1/3h}{v3}
\fmfforce{6/8w,0h}{v4}
\fmfforce{6/8w,2/3h}{v5}
\fmf{boson}{v4,v5}
\fmf{boson,left=1}{v2,v5}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.5}{v3,v2}
\fmf{plain,right=0.5}{v1,v3}
\fmf{fermion,right=0.5}{v5,v3}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=0.5}{v3,v4}
\fmfdot{v4,v2,v3,v5}
\end{fmfgraph}
\end{center}}
%
% #16
%
${\displaystyle \frac{1}{2}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,0h}{v1}
\fmfforce{1/10w,1h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v4}
\fmfforce{3/5w,1/2h}{v5}
\fmfforce{4/5w,1/2h}{v6}
\fmfforce{9/10w,0h}{v7}
\fmfforce{9/10w,1h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v3,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{boson,right=1}{v7,v8,v7}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #17
%
${\displaystyle \frac{1}{2}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,0h}{v1}
\fmfforce{1/10w,1h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v4}
\fmfforce{3/5w,1/2h}{v5}
\fmfforce{4/5w,1/2h}{v6}
\fmfforce{9/10w,0h}{v7}
\fmfforce{9/10w,1h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v4,v5}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{boson,right=1}{v8,v7,v8}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #18
%
$1$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,1h}{v2}
\fmfforce{4/16w,1/2h}{v3}
\fmfforce{8/16w,1/2h}{v4}
\fmfforce{12/16w,1/2h}{v5}
\fmfforce{1w,1/2h}{v6}
\fmf{boson}{v4,v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #19
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,12)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1/3h}{v2}
\fmfforce{1/3w,1/6h}{v3}
\fmfforce{2/3w,1/6h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1/3h}{v6}
\fmfforce{1/2w,1/3h}{v7}
\fmfforce{1/3w,5/6h}{v8}
\fmfforce{2/3w,5/6h}{v9}
\fmfforce{1/2w,2/3h}{v10}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,left=1}{v5,v6}
\fmf{boson}{v7,v10}
\fmf{fermion,right=1}{v9,v8}
\fmf{plain,right=1}{v8,v9}
\fmfdot{v3,v4,v7,v10}
\end{fmfgraph}
\end{center}} 
%
% #20
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,12)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1/3h}{v2}
\fmfforce{1/3w,1/6h}{v3}
\fmfforce{2/3w,1/6h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1/3h}{v6}
\fmfforce{1/2w,1/3h}{v7}
\fmfforce{1/3w,5/6h}{v8}
\fmfforce{2/3w,5/6h}{v9}
\fmfforce{1/2w,2/3h}{v10}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=1}{v3,v4}
\fmf{boson,left=1}{v5,v6,v5}
\fmf{boson}{v7,v10}
\fmf{fermion,right=1}{v9,v8}
\fmf{plain,right=1}{v8,v9}
\fmfdot{v3,v4,v7,v10}
\end{fmfgraph}
\end{center}} 
%
\end{fmffile}
%
\\ &&&&
%
\begin{fmffile}{gl4112d}
%
% #21
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,12)
\setval
\fmfforce{2/8w,0h}{v1}
\fmfforce{2/8w,1/3h}{v2}
\fmfforce{4/8w,1/6h}{v3}
\fmfforce{6/8w,0h}{v4}
\fmfforce{6/8w,1/3h}{v5}
\fmfforce{6/8w,2/3h}{v6}
\fmfforce{4/8w,5/6h}{v7}
\fmfforce{8/8w,5/6h}{v8}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.5}{v5,v3}
\fmf{fermion,right=0.5}{v3,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{boson}{v4,v6}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}
\end{center}} 
%
% #22
%
$1$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,12)
\setval
\fmfforce{6/8w,0h}{v1}
\fmfforce{6/8w,1/3h}{v2}
\fmfforce{4/8w,1/6h}{v3}
\fmfforce{2/8w,0h}{v4}
\fmfforce{2/8w,1/3h}{v5}
\fmfforce{2/8w,2/3h}{v6}
\fmfforce{0/8w,5/6h}{v7}
\fmfforce{4/8w,5/6h}{v8}
\fmfforce{0w,1/6h}{v9}
\fmf{plain,left=1}{v1,v2}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,right=0.5}{v3,v5}
\fmf{fermion,right=0.5}{v4,v3}
\fmf{fermion,right=1}{v5,v4}
\fmf{boson}{v4,v6}
\fmf{fermion,right=1}{v8,v7}
\fmf{plain,right=1}{v7,v8}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}
\end{center}} 
%
% #23
%
$1$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,16)
\setval
\fmfforce{1/3w,2/16h}{v1}
\fmfforce{2/3w,4/16h}{v2}
\fmfforce{2/3w,8/16h}{v3}
\fmfforce{2/3w,12/16h}{v4}
\fmfforce{1/3w,14/16h}{v5}
\fmfforce{1w,14/16h}{v6}
\fmfforce{1w,2/16h}{v7}
\fmf{boson}{v4,v3}
\fmf{fermion,right=1}{v1,v7}
\fmf{plain,right=0.5}{v7,v2}
\fmf{fermion,right=0.5}{v2,v1}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v3,v2}
\fmf{plain,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{boson,left=0.7}{v1,v3}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}\end{center}} 
%
% #24
%
$1$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,6)
\setval
\fmfforce{2/20w,0h}{v1}
\fmfforce{2/20w,2/3h}{v2}
\fmfforce{4/20w,1/3h}{v3}
\fmfforce{8/20w,1/3h}{v4}
\fmfforce{12/20w,1/3h}{v5}
\fmfforce{16/20w,1/3h}{v6}
\fmfforce{18/20w,0h}{v7}
\fmfforce{18/20w,2/3h}{v8}
\fmfforce{10/20w,2/3h}{v9}
\fmfforce{14/20w,2/3h}{v10}
\fmf{boson}{v4,v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmf{fermion,right=1}{v10,v9}
\fmf{plain,right=1}{v9,v10}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #25
%
${\displaystyle \frac{1}{2}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(16,10)
\setval
\fmfforce{2/16w,0h}{v1}
\fmfforce{2/16w,4/10h}{v2}
\fmfforce{4/16w,2/10h}{v3}
\fmfforce{8/16w,2/10h}{v4}
\fmfforce{12/16w,2/10h}{v5}
\fmfforce{14/16w,0h}{v6}
\fmfforce{14/16w,4/10h}{v7}
\fmfforce{1/2w,6/10h}{v8}
\fmfforce{6/16w,8/10h}{v9}
\fmfforce{10/16w,8/10h}{v10}
\fmf{boson}{v3,v4}
\fmf{boson}{v4,v5}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,left=1}{v6,v7}
\fmf{fermion,right=1}{v6,v7}
\fmf{fermion,right=1}{v4,v8}
\fmf{fermion,right=1}{v8,v4}
\fmf{plain,right=1}{v9,v10}
\fmf{fermion,right=1}{v10,v9}
\fmfdot{v3,v4,v5,v8}
\end{fmfgraph}\end{center}} 
%
\end{fmffile}
%
\\
$4$ & $1$ & $2$ & $0$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4120a}
%
% #1
%
${\displaystyle \frac{1}{8}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/4w,1/2h}{v2}
\fmfforce{2/4w,1/2h}{v3}
\fmfforce{3/4w,1/2h}{v4}
\fmfforce{4/4w,1/2h}{v5}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{boson,right=1}{v4,v5,v4}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v3,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmfdot{v2,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #2
%
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{1/8w,0h}{v1a}
\fmfforce{1/8w,1h}{v1b}
\fmfforce{1/4w,1/2h}{v2}
\fmfforce{2/4w,1/2h}{v3}
\fmfforce{3/4w,1/2h}{v4}
\fmfforce{4/4w,1/2h}{v5}
\fmfforce{7/8w,0h}{v6}
\fmfforce{7/8w,1h}{v7}
\fmf{fermion,right=1}{v1b,v1a}
\fmf{plain,left=1}{v1b,v1a}
\fmf{plain,right=1}{v7,v6}
\fmf{fermion,right=1}{v6,v7}
\fmf{boson,right=1}{v2,v3,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmfdot{v2,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #3
%
${\displaystyle \frac{1}{4}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,8)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1/2h}{v2}
\fmfforce{1/3w,1/4h}{v3}
\fmfforce{2/3w,1/4h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1/2h}{v6}
\fmfforce{1/2w,1/2h}{v7}
\fmfforce{1/2w,1h}{v8}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,left=1}{v5,v6}
\fmf{boson,right=1}{v7,v8,v7}
\fmfdot{v3,v4,v7}
\end{fmfgraph}
\end{center}} 
%
% #4
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{0w,0.3h}{v1}
\fmfforce{1w,0.3h}{v2}
\fmfforce{1/6w,0.8h}{v3}
\fmfforce{5/6w,0.8h}{v4}
\fmfforce{0.5w,0.6h}{v5}
\fmf{fermion,right=0.4}{v2,v5}
\fmf{fermion,right=0.4}{v5,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{boson,right=0.4}{v1,v2}
\fmf{boson,right=0.4}{v2,v1}
\fmf{fermion,right=1}{v4,v3}
\fmf{plain,right=1}{v3,v4}
\fmfdot{v1,v2,v5}
\end{fmfgraph}\end{center}} 
%
% #5
%
${\displaystyle \frac{1}{4}}$
%
\parbox{11mm}{\begin{center}
\begin{fmfgraph}(8,8)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/2w,1/2h}{v2}
\fmfforce{1w,1/2h}{v3}
\fmfforce{3/4w,1/2h}{v5}
\fmf{fermion,right=1}{v2,v1,v2}
\fmf{fermion,right=1}{v2,v3,v2}
\fmf{boson,left=1}{v1,v3,v1}
\fmfdot{v1,v2,v3}
\end{fmfgraph}
\end{center}}
%
\end{fmffile}
%
\\
%
$4$ & $2$ & $0$ & $2$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4202a}
%
% #1
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmf{boson}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v1,v3}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #2
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmfforce{1/2w,0h}{v7}
\fmfforce{1/2w,1h}{v8}
\fmf{boson}{v7,v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v4,v8}
\fmf{fermion,right=0.4}{v8,v3}
\fmf{fermion,right=0.4}{v3,v7}
\fmf{fermion,right=0.4}{v7,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v7,v8,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #3
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmfforce{1/2w,1h}{v7}
\fmf{boson,left=0.6}{v2,v7}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v2,v7,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #4
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmfforce{1/2w,1h}{v7}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{boson,left=0.6}{v7,v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v6,v7,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #5
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,4)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1h}{v2}
\fmfforce{1/3w,1/2h}{v3}
\fmfforce{2/3w,1/2h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1h}{v6}
\fmfforce{1/2w,1h}{v7}
\fmf{fermion,right=0.4}{v6,v4}
\fmf{fermion,right=0.4}{v3,v2}
\fmf{boson,left=0.5}{v2,v6}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{plain,right=1}{v2,v1}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v6,v2,v3,v4}
\end{fmfgraph}
\end{center}}
%
% #6
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(14,6)
\setval
\fmfforce{2/14w,1/6h}{v1}
\fmfforce{2/14w,5/6h}{v2}
\fmfforce{4/14w,1/2h}{v3}
\fmfforce{10/14w,1/2h}{v4}
\fmfforce{12/14w,1/6h}{v5}
\fmfforce{12/14w,5/6h}{v6}
\fmfforce{5/14w,0.9h}{v7}
\fmfforce{9/14w,0.9h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=0.32}{v4,v8}
\fmf{fermion,right=0.32}{v8,v7}
\fmf{boson,left=0.4}{v8,v7}
\fmf{fermion,right=0.25}{v7,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{plain,left=1}{v5,v6}
\fmf{fermion,right=1}{v5,v6}
\fmfdot{v3,v4,v7,v8}
\end{fmfgraph}
\end{center}} 
%
% #7
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,4)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{1w,0.5h}{v2}
\fmfforce{1/2w,0.8h}{v3}
\fmfforce{1/2w,0.2h}{v4}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,left=0.2}{v3,v2}
\fmf{fermion,left=0.2}{v1,v3}
\fmf{fermion,left=0.2}{v2,v4}
\fmf{fermion,left=0.2}{v4,v1}
\fmf{boson}{v3,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}\end{center}} 
%
\end{fmffile}
%
\no \\
&&&&
%
\begin{fmffile}{gl4202b}
%
% #8
%
${\displaystyle \frac{1}{4}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,4)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{1w,0.5h}{v2}
\fmfforce{1/2w,1.25h}{v3}
\fmfforce{1/2w,0.2h}{v4}
\fmf{fermion,right=0.4}{v2,v3}
\fmf{fermion,right=0.4}{v3,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,left=0.25}{v4,v1}
\fmf{fermion,left=0.25}{v2,v4}
\fmf{fermion,left=0.4}{v1,v2}
\fmf{boson,left=0.4}{v3,v4}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}\end{center}} 
%
% #9
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,4)
\setval
\fmfforce{0w,0.5h}{v1}
\fmfforce{1w,0.5h}{v2}
\fmfforce{1/4w,1.14h}{v3}
\fmfforce{3/4w,1.14h}{v4}
\fmf{boson,left=0.3}{v4,v3}
\fmf{fermion,right=0.3}{v2,v4}
\fmf{fermion,right=0.3}{v4,v3}
\fmf{fermion,right=0.3}{v3,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,left=0.4}{v1,v2}
\fmf{fermion,left=0.4}{v2,v1}
\fmfdot{v1,v2,v3,v4}
\end{fmfgraph}\end{center}} 
%
% #10
%
$1$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,0h}{v1}
\fmfforce{1/10w,1h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v4}
\fmfforce{3/5w,1/2h}{v5}
\fmfforce{4/5w,1/2h}{v6}
\fmfforce{9/10w,0h}{v7}
\fmfforce{9/10w,1h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v3,v4}
\fmf{fermion,right=1}{v4,v5}
\fmf{fermion,right=1}{v5,v4}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #11
%
${\displaystyle \frac{1}{2}}$
%
\parbox{23mm}{\begin{center}
\begin{fmfgraph}(20,4)
\setval
\fmfforce{1/10w,0h}{v1}
\fmfforce{1/10w,1h}{v2}
\fmfforce{1/5w,1/2h}{v3}
\fmfforce{2/5w,1/2h}{v4}
\fmfforce{3/5w,1/2h}{v5}
\fmfforce{4/5w,1/2h}{v6}
\fmfforce{9/10w,0h}{v7}
\fmfforce{9/10w,1h}{v8}
\fmf{fermion,right=1}{v2,v1}
\fmf{plain,right=1}{v1,v2}
\fmf{boson}{v4,v5}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v5,v6}
\fmf{fermion,right=1}{v6,v5}
\fmf{fermion,right=1}{v7,v8}
\fmf{plain,right=1}{v8,v7}
\fmfdot{v3,v4,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #12
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,14)
\setval
\fmfforce{0w,3/14h}{v1}
\fmfforce{1w,3/14h}{v2}
\fmfforce{1/6w,12/14h}{v3}
\fmfforce{5/6w,12/14h}{v4}
\fmfforce{0.5w,6/14h}{v5}
\fmfforce{0.5w,10/14h}{v6}
\fmf{fermion,right=0.4}{v2,v5}
\fmf{fermion,right=0.4}{v5,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,left=0.4}{v2,v1}
\fmf{fermion,left=0.4}{v1,v2}
\fmf{fermion,right=1}{v4,v3}
\fmf{plain,right=1}{v3,v4}
\fmf{boson}{v5,v6}
\fmfdot{v1,v2,v5,v6}
\end{fmfgraph}\end{center}} 
%
% #13
%
$1$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,12)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1/3h}{v2}
\fmfforce{1/3w,1/6h}{v3}
\fmfforce{2/3w,1/6h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1/3h}{v6}
\fmfforce{1/2w,1/3h}{v7}
\fmfforce{1/3w,5/6h}{v8}
\fmfforce{2/3w,5/6h}{v9}
\fmfforce{1/2w,2/3h}{v10}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,left=1}{v5,v6}
\fmf{boson}{v7,v10}
\fmf{fermion,right=1}{v9,v8}
\fmf{plain,right=1}{v8,v9}
\fmfdot{v3,v4,v7,v10}
\end{fmfgraph}
\end{center}} 
%
\end{fmffile}
%
\\
%
$4$ & $2$ & $1$ & $0$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4210a}
%
% #1
%
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{0w,1/2h}{v1}
\fmfforce{1/4w,1/2h}{v2}
\fmfforce{2/4w,1/2h}{v3}
\fmfforce{3/4w,1/2h}{v4}
\fmfforce{7/8w,0h}{v5}
\fmfforce{7/8w,1h}{v6}
\fmf{boson,right=1}{v1,v2,v1}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v3,v2}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,left=1}{v5,v6}
\fmfdot{v2,v3,v4}
\end{fmfgraph}
\end{center}} 
%
% #2
%
${\displaystyle \frac{1}{4}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{0w,0.3h}{v1}
\fmfforce{1w,0.3h}{v2}
\fmfforce{1/6w,0.8h}{v3}
\fmfforce{5/6w,0.8h}{v4}
\fmfforce{0.5w,0.6h}{v5}
\fmf{fermion,right=0.4}{v2,v5}
\fmf{fermion,right=0.4}{v5,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,left=0.4}{v1,v2}
\fmf{fermion,left=0.4}{v2,v1}
\fmf{boson,right=1}{v4,v3,v4}
\fmfdot{v1,v2,v5}
\end{fmfgraph}\end{center}} 
%
% #3
%
${\displaystyle \frac{1}{2}}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,8)
\setval
\fmfforce{1/6w,0h}{v1}
\fmfforce{1/6w,1/2h}{v2}
\fmfforce{1/3w,1/4h}{v3}
\fmfforce{2/3w,1/4h}{v4}
\fmfforce{5/6w,0h}{v5}
\fmfforce{5/6w,1/2h}{v6}
\fmfforce{1/2w,1/2h}{v7}
\fmfforce{1/2w,1h}{v8}
\fmf{plain,right=1}{v1,v2}
\fmf{fermion,right=1}{v2,v1}
\fmf{fermion,right=0.4}{v7,v3}
\fmf{fermion,right=0.4}{v4,v7}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v5,v6}
\fmf{plain,left=1}{v5,v6}
\fmf{boson,right=1}{v7,v8,v7}
\fmfdot{v3,v4,v7}
\end{fmfgraph}
\end{center}} 
%
\end{fmffile}
%
\\
%
$4$ & $3$ & $0$ & $0$ &
\hspace{-10pt}
\rule[-10pt]{0pt}{26pt}
%
\begin{fmffile}{gl4300a}
%
% #1
%
$\frac{1}{6}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,6)
\setval
\fmfforce{0.5w,1h}{v1}
\fmfforce{0.066987w,0.25h}{v2}
\fmfforce{0.93301w,0.25h}{v3}
\fmf{fermion,right=0.5}{v1,v2}
\fmf{fermion,right=0.5}{v2,v3}
\fmf{fermion,right=0.5}{v3,v1}
\fmf{fermion}{v1,v3}
\fmf{fermion}{v3,v2}
\fmf{fermion}{v2,v1}
\fmfdot{v2,v3,v1}
\end{fmfgraph}
\end{center}} 
%
% #2
%
$\frac{1}{24}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,6)
\setval
\fmfforce{0.5w,1h}{v1}
\fmfforce{0.066987w,0.25h}{v2}
\fmfforce{0.93301w,0.25h}{v3}
\fmf{fermion,right=0.5}{v1,v2}
\fmf{fermion,right=0.5}{v2,v3}
\fmf{fermion,right=0.5}{v3,v1}
\fmf{fermion}{v3,v1}
\fmf{fermion}{v2,v3}
\fmf{fermion}{v1,v2}
\fmfdot{v2,v3,v1}
\end{fmfgraph}
\end{center}} 
%
% #3
%
${\displaystyle \frac{1}{2}}$
%
\parbox{9mm}{\begin{center}
\begin{fmfgraph}(6,10)
\setval
\fmfforce{0w,0.3h}{v1}
\fmfforce{1w,0.3h}{v2}
\fmfforce{1/6w,0.8h}{v3}
\fmfforce{5/6w,0.8h}{v4}
\fmfforce{0.5w,0.6h}{v5}
\fmf{fermion,right=0.4}{v2,v5}
\fmf{fermion,right=0.4}{v5,v1}
\fmf{fermion,right=1}{v1,v2}
\fmf{fermion,left=0.4}{v1,v2}
\fmf{fermion,left=0.4}{v2,v1}
\fmf{fermion,right=1}{v4,v3}
\fmf{plain,right=1}{v3,v4}
\fmfdot{v1,v2,v5}
\end{fmfgraph}\end{center}} 
%
% #4
%
$\frac{1}{3}$
%
\parbox{15mm}{\begin{center}
\begin{fmfgraph}(12,12)
\setval
\fmfforce{1/2w,1/3h}{v1}
\fmfforce{1/2w,2/3h}{v2}
\fmfforce{4/12w,10/12h}{v3a}
\fmfforce{8/12w,10/12h}{v3b}
\fmfforce{0.355662432w,0.416666666h}{v4}
\fmfforce{0.64433568w,0.416666666h}{v5}
\fmfforce{0.127997882w,0.477709013h}{v6}
\fmfforce{0.294664549w,0.188995765h}{v7}
\fmfforce{0.87200023w,0.477709013h}{v8}
\fmfforce{0.705333563w,0.188995765h}{v9}
\fmf{fermion,right=0.55}{v2,v4}
\fmf{fermion,right=0.55}{v4,v5}
\fmf{fermion,right=0.55}{v5,v2}
\fmf{fermion,right=1}{v3b,v3a}
\fmf{plain,right=1}{v3a,v3b}
\fmf{fermion,right=1}{v6,v7}
\fmf{plain,right=1}{v7,v6}
\fmf{fermion,right=1}{v9,v8}
\fmf{plain,right=1}{v8,v9}
\fmfdot{v2,v4,v5}
\end{fmfgraph}\end{center}} 
%
% #5
% 
${\displaystyle \frac{1}{2}}$
%
\parbox{19mm}{\begin{center}
\begin{fmfgraph}(16,4)
\setval
\fmfforce{1/8w,1h}{v1a}
\fmfforce{1/8w,0h}{v1b}
\fmfforce{1/4w,0.5h}{v2}
\fmfforce{2/4w,0.5h}{v3}
\fmfforce{3/4w,0.5h}{v4}
\fmfforce{7/8w,1h}{v5a}
\fmfforce{7/8w,0h}{v5b}
\fmf{fermion,right=1}{v1a,v1b}
\fmf{plain,left=1}{v1a,v1b}
\fmf{fermion,right=1}{v3,v2}
\fmf{fermion,right=1}{v2,v3}
\fmf{fermion,right=1}{v4,v3}
\fmf{fermion,right=1}{v3,v4}
\fmf{fermion,right=1}{v5b,v5a}
\fmf{plain,right=1}{v5a,v5b}
\fmfdot{v2,v3,v4}
\end{fmfgraph}\end{center}}
%
\end{fmffile}
%
\end{tabular}
\end{center}
\caption{Connected vacuum diagrams $W^{(L,n_1,n_2,n_3)}$ and their weights up to the four-loop order
of the $O(2)$ \gl model, wehre $L$ denotes the loop order and $n_1,n_2,n_3$ count the number of vertices
$V,F,H$, respectively.}
\end{table}


\end{document}

