\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{physics}

\usepackage{feynmp}
\DeclareGraphicsRule{*}{mps}{*}{}

\begin{document}

\begin{center}
	{\Huge \sc Feynman diagrams}
\end{center}

\noindent
Full Green's function
\begin{align*}
\hbar G(b,a)
&= \quad
\begin{fmffile}{0order1}
	\begin{fmfgraph*}(30,20)
		\fmfipair{i,o}
		\fmfiequ{i}{(0w,0.3h)}
		\fmfiequ{o}{(1w,0.3h)}
		\fmfi{fermion}{i -- o}
		\fmfiv{decor.shape=circle,decor.size=4,label=$a$,label.angle=-90}{i}
		\fmfiv{decor.shape=circle,decor.size=4,label=$b$,label.angle=-90}{o}
	\end{fmfgraph*}
\end{fmffile}
\quad + \quad
\begin{fmffile}{1order1}
	\begin{fmfgraph*}(50,20)
		\fmfipair{i,m,t,t',o}
		\fmfiequ{i}{(0w,0.3h)}
		\fmfiequ{m}{(0.5w,0.3h)}
		\fmfiequ{t}{(0.5w,0.9h)}
		\fmfiequ{t'}{(0.5w,1.3h)}
		\fmfiequ{o}{(1w,0.3h)}
		\fmfi{fermion}{i -- m}
		\fmfi{boson}{m -- t}
		\fmfi{plain}{t{left} .. {right}t'}
		\fmfi{plain}{t'{right} .. {left}t}
		\fmfi{fermion}{m -- o}
		\fmfiv{decor.shape=circle,decor.size=4,label=$a$,label.angle=-90}{i}
		\fmfiv{decor.shape=circle,decor.size=4}{m}
		\fmfiv{decor.shape=circle,decor.size=4}{t}
		\fmfiv{decor.shape=circle,decor.size=4,label=$b$,label.angle=-90}{o}
	\end{fmfgraph*}
\end{fmffile}
\quad + \quad
\begin{fmffile}{1order2}
	\begin{fmfgraph*}(70,20)
		\fmfipair{i,a,b,o}
		\fmfiequ{i}{(0w,0.3h)}
		\fmfiequ{a}{(0.33w,0.3h)}
		\fmfiequ{b}{(0.67w,0.3h)}
		\fmfiequ{o}{(1w,0.3h)}
		\fmfi{fermion}{i -- a}
		\fmfi{boson}{a -- b}
		\fmfi{fermion}{a{up} .. {down}b}
		\fmfi{fermion}{b -- o}
		\fmfiv{decor.shape=circle,decor.size=4,label=$a$,label.angle=-90}{i}
		\fmfiv{decor.shape=circle,decor.size=4}{a}
		\fmfiv{decor.shape=circle,decor.size=4}{b}
		\fmfiv{decor.shape=circle,decor.size=4,label=$b$,label.angle=-90}{o}
	\end{fmfgraph*}
\end{fmffile}
\quad + \:\: \cdots
\end{align*}
Self-energy definition
\begin{align*}
\frac{\Sigma(y,x)}{\hbar}
=\!\!\!\!
\begin{fmffile}{selfenergy}
	\begin{fmfgraph*}(20,20)
		\fmfright{v}
		\fmfv{label=$x\!\!\to\!\!y$,label.angle=-90,label.dist=10}{v}
		\fmfblob{15}{v}
	\end{fmfgraph*}
\end{fmffile}
&\quad\: \equiv \:\:\:\:
\begin{fmffile}{hartree}
	\begin{fmfgraph*}(25,20)
		\fmfleft{i}
		\fmfright{o}
		\fmf{boson}{i,o}
		\fmf{fermion}{o,o}
		\fmfv{label=$\:\:x\!\!=\!\!y$,label.angle=-90}{i}
		\fmfdot{i}
		\fmfdot{o}
	\end{fmfgraph*}
\end{fmffile}
\qquad + \:\:\:
\begin{fmffile}{fock}
	\begin{fmfgraph*}(40,20)
		\fmfipair{i,o}
		\fmfiequ{i}{(0,0.3h)}
		\fmfiequ{o}{(w,0.3h)}
		\fmfi{boson}{i -- o}
		\fmfi{fermion}{i{up} .. tension 1.5 .. {down}o}
		\fmfiv{decor.shape=circle,decor.size=4,label=$x$,label.angle=-90,label.dist=5}{i}
		\fmfiv{decor.shape=circle,decor.size=4,label=$y$,label.angle=-90,label.dist=5}{o}
	\end{fmfgraph*}
\end{fmffile}
\:\:\: + \:\:\:
\begin{fmffile}{pairbubble}
	\begin{fmfgraph*}(40,20)
		\fmfipair{i,a,b,o}
		\fmfiequ{i}{(0,0h)}
		\fmfiequ{a}{(0,1h)}
		\fmfiequ{b}{(1w,1h)}
		\fmfiequ{o}{(1w,0h)}
		\fmfi{fermion}{i -- o}
		\fmfi{boson}{i -- a}
		\fmfi{boson}{b -- o}
		\fmfi{fermion}{a{up} .. tension 2.5 .. {down}b}
		\fmfi{fermion}{b{down} .. tension 2.5 .. {up}a}
		\fmfiv{decor.shape=circle,decor.size=4,label=$x$,label.angle=-90,label.dist=5}{i}
		\fmfiv{decor.shape=circle,decor.size=4,label.angle=-90,label.dist=3}{a}
		\fmfiv{decor.shape=circle,decor.size=4,label.angle=-90,label.dist=3}{b}
		\fmfiv{decor.shape=circle,decor.size=4,label=$y$,label.angle=-90,label.dist=5}{o}
	\end{fmfgraph*}
\end{fmffile}
\:\:\: + \: \cdots
\end{align*}
Dyson equation
\begin{align*}
\hbar G(b,a)
= \quad
\begin{fmffile}{fullgf}
	\begin{fmfgraph*}(50,20)
		\fmfleft{i}
		\fmfright{o}
		\fmf{heavy}{i,o}
		\fmfv{label=$a$,label.angle=-90}{i}
		\fmfv{label=$b$,label.angle=-90}{o}
		\fmfdot{i}
		\fmfdot{o}
	\end{fmfgraph*}
\end{fmffile}
\quad = \quad
\begin{fmffile}{freegf}
	\begin{fmfgraph*}(50,20)
		\fmfleft{i}
		\fmfright{o}
		\fmf{fermion}{i,o}
		\fmfv{label=$a$,label.angle=-90}{i}
		\fmfv{label=$b$,label.angle=-90}{o}
		\fmfdot{i}
		\fmfdot{o}
	\end{fmfgraph*}
\end{fmffile}
\quad + \quad
\begin{fmffile}{dyson}
	\begin{fmfgraph*}(110,20)
		\fmfleft{i}
		\fmfright{o}
		\fmf{fermion}{i,v}
		\fmf{heavy}{v,o}
		\fmfv{label=$a$,label.angle=-90}{i}
		\fmfv{label=$b$,label.angle=-90}{o}
		\fmfdot{i}
		\fmfdot{o}
		\fmfv{label=$x\!\to\!y$,label.angle=-90,label.dist=10}{v}
		\fmfblob{15}{v}
	\end{fmfgraph*}
\end{fmffile}
\end{align*}

\end{document}