Tikz-Feynman Diagrams

\vertex (t0);

\vertex [right=of t0] (t1);

\vertex [right=of t1] (t);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

};

\vertex (t0);

\vertex [right=of t0] (t1);

\vertex [right=of t1] (t);

\vertex [above=of t1] (p1);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t1) -- [boson1, edge label'={\(q=0\)}, inner sep=1.5mm] (p1),

};

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p1) arc (270:-270:0.75) node[label={[yshift=-1mm]\(p,\omega'_n\)}];

\fill (t1) circle (1pt);

\fill (p1) circle (1pt);

\vertex (t0);

\vertex [right=1.25cm of t0] (t1);

\vertex [right=2.0cm of t1] (t2);

\vertex [right=1.25cm of t2] (t);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label={\(k-q\)}, inner sep=0.85mm] (t2) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'={\(\omega'_n\)}, inner sep=1.5mm] (t2) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t1) -- [boson] (t2),

};

\vertex [above right=1.05cm and 0.75cm of t1] {\(q\)};

\fill (t1) circle (1pt);

\fill (t2) circle (1pt);

\vertex (t0);

\vertex [right=of t0] (t1);

\vertex [right=of t1] (t2);

\vertex [right=of t2] (t3);

\vertex [right=of t3] (t);

\vertex [above=of t1] (p1);

\vertex [above=of t3] (p3);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t3) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t3) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t1) -- [boson1, edge label'={\(q=0\)}, inner sep=1.5mm] (p1),

(t3) -- [boson1, edge label'={\(q'=0\)}, inner sep=1.5mm] (p3),

};

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p1) arc (270:-270:0.75) node[label={[yshift=-1mm]\(p,\omega_n'\)}];

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p3) arc (270:-270:0.75) node[label={[yshift=-1mm]\(p',\omega_n''\)}];

\fill (t1) circle (1pt);

\fill (t3) circle (1pt);

\fill (p1) circle (1pt);

\fill (p3) circle (1pt);

\vertex (t0);

\vertex [right=1cm of t0] (t1);

\vertex [right=2cm of t1] (t2);

\vertex [right=1.25cm of t2] (t3);

\vertex [right=2cm of t3] (t4);

\vertex [right=1cm of t4] (t);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label={\(k-q\)}, inner sep=0.85mm] (t2) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t3) -- [fermion, edge label={\(k-q'\)}, inner sep=0.85mm] (t4) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'={\(\omega_n'\)}, inner sep=0.85mm] (t2) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t3) -- [fermion, edge label'={\(\omega_n''\)}, inner sep=0.85mm] (t4) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t1) -- [boson] (t2),

(t3) -- [boson] (t4),

};

\vertex [above right=1.05cm and 0.75cm of t1] {\(q\)};

\vertex [above right=1.05cm and 0.75cm of t3] {\(q'\)};

\fill (t1) circle (1pt);

\fill (t2) circle (1pt);

\fill (t3) circle (1pt);

\fill (t4) circle (1pt);

\vertex (t0);

\vertex [right=of t0] (t1);

\vertex [right=of t1] (t2);

\vertex [right=2cm of t2] (t3);

\vertex [right=1.25cm of t3] (t);

\vertex [above=of t1] (p1);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t2) -- [fermion, edge label={\(k-q'\)}, inner sep=0.85mm] (t3) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t2) -- [fermion, edge label'={\(\omega_n''\)}, inner sep=0.85mm] (t3) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t1) -- [boson1, edge label'={\(q=0\)}, inner sep=1.5mm] (p1),

(t2) -- [boson] (t3),

};

\vertex [above right=1.05cm and 0.75cm of t2] {\(q'\)};

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p1) arc (270:-270:0.75) node[label={[yshift=-1mm]\(p,\omega_n'\)}];

\fill (t1) circle (1pt);

\fill (t2) circle (1pt);

\fill (t3) circle (1pt);

\fill (p1) circle (1pt);

\vertex (t0);

\vertex [right=1.25cm of t0] (t1);

\vertex [right=2cm of t1] (t2);

\vertex [right=of t2] (t3);

\vertex [right=of t3] (t);

\vertex [above=of t3] (p3);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label={\(k-q\)}, inner sep=0.85mm] (t2) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t3) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'={\(\omega_n'\)}, inner sep=0.85mm] (t2) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t3) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t1) -- [boson] (t2),

(t3) -- [boson1, edge label'={\(q'=0\)}, inner sep=1.5mm] (p3),

};

\vertex [above right=1.05cm and 0.75cm of t1] {\(q\)};

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p3) arc (270:-270:0.75) node[label={[yshift=-1mm]\(p',\omega_n''\)}];

\fill (t1) circle (1pt);

\fill (t2) circle (1pt);

\fill (t3) circle (1pt);

\fill (p3) circle (1pt);

\vertex (t0);

\vertex [right=of t0] (t1);

\vertex [right=of t1] (t);

\vertex [above=of t1] (p1);

\vertex [above=of p1] (q1);

\vertex [above=of q1] (r1);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t1) -- [boson1, edge label'={\(q=0\)}, inner sep=1.5mm] (p1),

(q1) -- [boson1, edge label'={\(q'=0\)}, inner sep=1.5mm] (r1),

};

\vertex [above=of p1] (q1);

\draw (p1) arc (270:-270:0.75);

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p1) arc (270:180:0.75) node[label={[xshift=-5mm,yshift=-4mm]\(p,\omega_n'\)}];

\draw [-{>[flex=1.25]}, shorten >=-4pt] (q1) arc (90:0:0.75) node[label={[xshift=5.5mm,yshift=-4mm]\(p,\omega_n'\)}];

\draw [-{>[flex=1.25]}, shorten >=-4pt] (r1) arc (270:-270:0.75) node[label={[yshift=-1mm]\(p',\omega_n''\)}];

\fill (t1) circle (1pt);

\fill (p1) circle (1pt);

\fill (q1) circle (1pt);

\fill (r1) circle (1pt);

\vertex (t0);

\vertex [right= of t0] (t1);

\vertex [right=of t1] (t);

\vertex [above=of t1] (p1);

\vertex [above left=0.75cm and 0.75cm of p1] (q1);

\vertex [above right=0.75cm and 0.75cm of p1] (q2);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t1) -- [boson1, edge label'={\(q=0\)}, inner sep=1.5mm] (p1),

(q1) -- [boson1, edge label=\(q'\), inner sep=1.5mm] (q2),

};

\draw (p1) arc (270:-270:0.75);

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p1) arc (270:225:0.75) node[label={[xshift=-5mm,yshift=-6mm]\(p,\omega_n'\)}];

\draw [-{>[flex=1.25,reversed]}, shorten >=-4pt] (p1) arc (270:315:0.75) node[label={[xshift=5.5mm,yshift=-6mm]\(p,\omega_n'\)}];

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p1) arc (270:90:0.75) node[label={[yshift=-1mm]\(p+q',\omega_n''\)}];

\fill (t1) circle (1pt);

\fill (p1) circle (1pt);

\fill (q1) circle (1pt);

\fill (q2) circle (1pt);

\vertex (t0);

\vertex [right=of t0] (t1);

\vertex [right=of t1] (t2);

\vertex [right=of t2] (t3);

\vertex [right=of t3] (t);

\vertex [above=of t2] (p2);

\diagram* {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label={\(k-q\)}, inner sep=0.85mm] (t2) -- [fermion, edge label={\(k-q\)}, inner sep=0.85mm] (t3) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'={\(\omega_n'\)}, inner sep=0.85mm] (t2) -- [fermion, edge label'={\(\omega_n'\)}, inner sep=0.85mm] (t3) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t3) -- [boson] (t1),

(t2) -- [boson1, edge label'={\(q'=0\)}, inner sep=1.5mm] (p2),

};

\vertex [below=1.6cm of t2] {\(q\)};

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p2) arc (270:-270:0.75) node[label={[yshift=-1mm]\(p,\omega_n''\)}];

\fill (t1) circle (1pt);

\fill (t2) circle (1pt);

\fill (t3) circle (1pt);

\fill (p2) circle (1pt);

\vertex (t0);

\vertex [right=1cm of t0] (t1);

\vertex [right=of t1] (t2);

\vertex [right=2.5cm of t2] (t3);

\vertex [right=of t3] (t4);

\vertex [right=1cm of t4] (t);

\diagram {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label={\(k-q\)}, inner sep=0.85mm] (t2) -- [fermion, edge label={\(k-q-q'\)}, inner sep=0.85mm] (t3) -- [fermion, edge label={\(k-q'\)}, inner sep=0.85mm] (t4) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'={\(\omega_n'\)}, inner sep=0.85mm] (t2) -- [fermion, edge label'={\(\omega_n''\)}, inner sep=0.85mm] (t3) -- [fermion, edge label'={\(\omega_n'\)}, inner sep=0.85mm] (t4) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t3) -- [boson2] (t1),

(t2) -- [boson2] (t4),

};

\vertex [below right=2.1cm and 0.25cm of t2] {\(q\)};

\vertex [above left=2.1cm and 0.15cm of t3] {\(q'\)};

\fill (t1) circle (1pt);

\fill (t2) circle (1pt);

\fill (t3) circle (1pt);

\fill (t4) circle (1pt);

\vertex (t0);

\vertex [right=1cm of t0] (t1);

\vertex [right=of t1] (t2);

\vertex [right=2.5cm of t2] (t3);

\vertex [right=of t3] (t4);

\vertex [right=1cm of t4] (t);

\diagram* {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label={\(k-q\)}, inner sep=0.85mm] (t2) -- [fermion, edge label={\(k-q-q'\)}, inner sep=0.85mm] (t3) -- [fermion, edge label={\(k-q\)}, inner sep=0.85mm] (t4) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'={\(\omega_n'\)}, inner sep=0.85mm] (t2) -- [fermion, edge label'={\(\omega_n''\)}, inner sep=0.85mm] (t3) -- [fermion, edge label'={\(\omega_n'\)}, inner sep=0.85mm] (t4) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(t2) -- [boson] (t3),

(t1) -- [boson3] (t4),

};

\vertex [above right=2.8cm and 1cm of t2] {\(q\)};

\vertex [above right=1.3cm and 1cm of t2] {\(q'\)};

\fill (t1) circle (1pt);

\fill (t2) circle (1pt);

\fill (t3) circle (1pt);

\fill (t4) circle (1pt);

\vertex (t0);

\vertex [right=of t0] (t1);

\vertex [right=of t1] (t2);

\vertex [right=of t2] (t3);

\vertex [right=of t3] (t);

\vertex [above=2.5cm of t1] (p1);

\vertex [above=2.5cm of t3] (p3);

\diagram* {

(t0) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t1) -- [fermion, edge label={\(k-q\)}, inner sep=1.5mm] (t3) -- [fermion, edge label=\(k\), inner sep=1.5mm] (t),

(t0) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t1) -- [fermion, edge label'={\(\omega_n'\)}, inner sep=1.5mm] (t3) -- [fermion, edge label'=\(\omega_n\), inner sep=1.5mm] (t),

(p1) -- [fermion, out=45, in=135, edge label={\(p+q,\omega_n'''\)}, inner sep=1.5mm] (p3),

(p3) -- [fermion, out=-135, in=-45, edge label={\(p,\omega_n''\)}, inner sep=1.5mm] (p1),

(t1) -- [boson1, edge label'={\(q\)}, inner sep=1.5mm] (p1),

(t3) -- [boson1, edge label'={\(q\)}, inner sep=1.5mm] (p3),

};

\fill (t1) circle (1pt);

\fill (t3) circle (1pt);

\fill (p1) circle (1pt);

\fill (p3) circle (1pt);

$\vcenter{\hbox{

\begin{tikzpicture} [thick, >=Latex]

\begin{feynman}

\vertex [label={[yshift=0.05cm]\(\mbox{\Huge$\Sigma$}\)}] (t0);

\draw (t0) arc (270:-270:0.5);

\end{feynman}

\end{tikzpicture}}}$

$\Huge{\raisebox{-4pt}{\,=}}$

$\vcenter{\hbox{

\begin{tikzpicture} [thick, >=Latex]

\begin{feynman}

\vertex (t0);

\vertex [right=of t0] (t1);

\vertex [left=2.5pt of t1] (t2);

\vertex [right=2.5pt of t1] (t3);

\vertex [above=of t1] (p1);

\vertex [above=of t2] (p2);

\vertex [above=of t3] (p3);

\vertex [above=4pt of p1] (p4);

\diagram {

(t2) -- [boson1] (p2),

(t3) -- [boson1] (p3),

};

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p1) arc (270:-270:0.75);

\draw [-{>[flex=1.25]}, shorten >=-4pt] (p4) arc (270:-270:0.60);

\fill (t2) circle (1pt);

\fill (t3) circle (1pt);

\fill (p2) circle (1pt);

\fill (p3) circle (1pt);

\end{feynman}

\end{tikzpicture}}}$

$\Huge{\raisebox{-4pt}{+}}$

$\vcenter{\hbox{

\begin{tikzpicture} [thick, >=Latex]

\begin{feynman}

\vertex (t0);

\vertex [right=5pt of t0] (t1);

\vertex [right=of t1] (t2);

\vertex [right=5pt of t2] (t3);

\diagram {

(t0) -- [doublefermion] (t3),

(t0) -- [boson0] (t3),

(t1) -- [boson0] (t2),

};

\draw [red,fill=orange] (t1) circle (10pt);

\fill (t2) circle (1pt);

\fill (t3) circle (1pt);

\end{feynman}

\end{tikzpicture}}}$