From 6505b1fb3399ec4bff97aabda2554764bf305d0f Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sun, 21 Nov 2021 18:02:35 +0100
Subject: Expand knowledge base

---
 sources/know/concept/self-energy/main.tex | 171 ++++++++++++++++++++++++++++++
 1 file changed, 171 insertions(+)
 create mode 100644 sources/know/concept/self-energy/main.tex

(limited to 'sources/know/concept/self-energy/main.tex')

diff --git a/sources/know/concept/self-energy/main.tex b/sources/know/concept/self-energy/main.tex
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@@ -0,0 +1,171 @@
+\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}
+	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}
+\Sigma(y,x)
+=\!\!\!\!
+\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}
+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}
-- 
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