在 LaTeX 中绘制费曼图 - LaTeX - 计算机科学 | White Album = 白色相簿 = 梦里不觉秋已深，余情岂是为他人

通常使用 TikZ-Feynman^[1] 绘制费曼图^[2]比 axodraw 和 feynMF/feynMP 要容易许多，那俩语法稍微复杂，适合绘制更复杂的费曼图。这里我们需要的场景不用那么麻烦。如果你在论文或书籍里使用了这个宏包，请引用：doi:10.1016/j.cpc.2016.08.019 或 arXiv:1601.05437。

# 配置环境

这里我们使用 VSCode 编辑器配合 MikTeX 搭建我们的 $\LaTeX$ 编写环境。

在 VSCode 配置文件 settings.json 中加入：

settings.json

	{
	"latex-workshop.latex.tools": [// 编译工具和命令
	{
	"name": "lualatex",
	"command": "lualatex",
	"args": [
	"-synctex=1",
	"-interaction=nonstopmode",
	"-file-line-error",
	"-shell-escape",// 这一项需要谨慎，有可能会运行不安全的代码
	"-output-directory=%OUTDIR%",
	"%DOC%"
	]
	}
	],
	"latex-workshop.latex.recipes": [// 用于配置编译链
	{
	"name": "LuaLaTeX",
	"tools": ["lualatex"]
	}
	]
	}

关于我更详细的配置请查看 LaTeX 环境配置。

引用 TikZ-Feynman 宏包后请在编译链中再用 LuaLaTeX 编译一次。

lualatex -interaction=nonstopmode -shell-escape main.tex

\usepackage[compat=1.1.0]{tikz-feynman}

使用 compat 选项是为了版本兼容性，如果不使用此项会有警告。这个包最后一次更新是 2016 年^[3]，还算稳定。

# 示例

遇到问题，查文档（很多人就是不看文档.jpg）：

文档是你的好朋友！

texdoc tikz-feynman

# 线的类型

图像	类型	名称
	plain	普通直线
	boson	玻色子线
	charged boson	带电玻色子线
	anti charged boson	反带电玻色子线
	photon	光子线
	scalar	标量线
	charged scalar	带电标量线
	anti charged scalar	反带电标量线
	ghost	鬼线
	fermion	费米子线
	anti fermion	反费米子线
	majorana	马约拉纳费米子线
	anti majorana	反马约拉纳费米子线
	gluon	胶子线

fig:01

	\feynmandiagram[horizontal=a to b]{
	i1 -- [fermion] a -- [fermion] i2,
	a -- [photon] b,
	f1 -- [fermion] b -- [fermion] f2,
	};

\feynmandiagram[]{}; 指令即引入费曼图， horizontal 选项就是指中间 a 点到 b 点是水平线；
路径 i1 -> a -> i2 即指左下角 i1 点到中间 a 点再到左上角 i2 点，线的类型都是费米子线 [fermion] ；
路径 a -> b 即指中间 a 点水平向右指向中间 b 点，线的类型是光子线 [photon] ；
路径 f1 -> b -> f2 即指右上角 f1 点到中间 b 点再到右下角 f2 点，线的类型都是费米子线 [fermion] ；
; 结束费曼图环境。

fig:02

	\feynmandiagram[horizontal=f2 to f3]{
	f1 -- [fermion] f2 -- [fermion] f3 -- [fermion] f4,
	f2 -- [photon] p1,
	f3 -- [photon] p2,
	};

路径 f1 -> f2 -> f3 -> f4 即指左下角 f1 点到中间 f2 点再到中间 f3 点再到右上角 f4 点，线的类型都是费米子线 [fermion] ；
路径 f2 -> p1 即指中间 f2 点指向左上角 p1 点，线的类型是光子线 [photon] ；
路径 f2 -> p1 即指中间 f3 点指向右下角 p2 点，线的类型是光子线 [photon] 。

fig:03

	\feynmandiagram[horizontal=a to b]{
	i1 [particle=$e^{-}$] -- [fermion] a -- [fermion] i2 [particle=$e^{+}$],
	a -- [photon, edge label=$\gamma$, momentum'=$k$] b,
	f1 [particle=$\mu^{+}$] -- [fermion] b -- [fermion] f2 [particle=$\mu^{-}$],
	};

fig:04

	\feynmandiagram[horizontal=a to b]{
	i1 [particle=$e^{-}$] -- [fermion,very thick] a -- [fermion,opacity=0.2] i2 [particle=$e^{+}$],
	a -- [photon,red,edge label=$\gamma$,momentum'={[arrow style=red]$k$}] b,
	f1 [particle=$\mu^{+}$] -- [fermion,opacity=0.2] b -- [fermion,very thick] f2 [particle=$\mu^{-}$],
	};

fig:05

	\feynmandiagram[horizontal=a to b]{
	i1 [particle=$\tilde{W}$] -- [plain, boson] a -- [anti fermion] i2 [particle=$q$],
	a -- [charged scalar,edge label=$\tilde{q}$] b,
	f1 [particle=$\tilde{g}$] -- [plain, gluon] b -- [fermion] f2 [particle=$q$],
	};

fig:06

	\feynmandiagram[horizontal=a to t1]{
	a [particle=$\pi^{0}$] -- [scalar] t1 -- t2 -- t3 -- t1,
	t2 -- [photon] p1 [particle=$\gamma$],
	t3 -- [photon] p2 [particle=$\gamma$],
	};

fig:07

	\feynmandiagram[horizontal=a to t1]{
	a [particle=$\pi^{0}$] -- [scalar] t1 -- t2 -- t3 -- t1,
	t2 --[photon] p1 [particle=$\gamma$],
	t3 --[photon] p2 [particle=$\gamma$],
	p1 -- [opacity=0.2] p2,
	};

fig:08

	\feynmandiagram[horizontal=a to b]{
	a [particle=$\mu^{-}$] -- [fermion] b -- [fermion] f1 [particle=$\nu_{\mu}$],
	b -- [boson,edge label=$W^{-}$] c,
	f2 [particle=$\overline{\nu_{e}}$] -- [fermion] c -- [fermion] f3 [particle=$e^{-}$],
	};

fig:09

	\feynmandiagram[layered layout,horizontal=a to b]{
	a [particle=$\mu^{-}$] -- [fermion] b -- [fermion] f1 [particle=$\nu_{\mu}$],
	b -- [boson,edge label=$W^{-}$] c,
	c -- [anti fermion] f2 [particle=$\overline{\nu_{e}}$],
	c -- [fermion] f3 [particle=$e^{-}$],
	};

fig:10

	\begin{tikzpicture}
	\begin{feynman}
	\vertex(a) {$\mu^{-}$};
	\vertex[right=of a](b);
	\vertex[above right=of b](f1){$\nu_{\mu}$};
	\vertex[below right=of b](c);
	\vertex[above right=of c](f2){$\overline{\nu_{e}}$};
	\vertex[below right=of c](f3){$e^{-}$};

	\diagram*{
	(a)--[fermion](b)--[fermion](f1),
	(b)--[boson,edge label'=$W^{-}$](c),
	(c)--[anti fermion](f2),
	(c)--[fermion](f3),
	};
	\end{feynman}
	\end{tikzpicture}

fig:11

	\feynmandiagram[nodes=circle,horizontal=a1 to b3]{
	a1 -- {b1,b2,b3 -- {c1,c2 -- d1}},
	};

fig:12

	\feynmandiagram[nodes=circle,small,horizontal=a to b,tree layout]{
	a -- b -- {c -- {c1,c2},d -- {d1,d2}},
	};

fig:13

	\tikzfeynmanset{every feynman={red}}
	\begin{center}
	\begin{tikzpicture}
	\node at (0,0.5){This is LZU};
	\begin{feynman}
	\node at (0,-0.5){This is LZU};
	\end{feynman}
	\end{tikzpicture}

fig:14

	\begin{equation}
	\feynmandiagram[inline=(d.base),horizontal=d to b]{
	a -- [fermion] b -- [fermion] c,
	b -- [boson] d [particle=\gamma],
	};
	=ig_{e}\gamma^{\mu}\notag
	\end{equation}

fig:15

	\begin{equation}
	\feynmandiagram[baseline=(d.base),horizontal=d to b]{
	a -- [fermion] b -- [fermion] c,
	b -- [boson] d [particle=\gamma],
	};
	=ig_{e}\gamma^{\mu}\notag
	\end{equation}

fig:16-1
fig:16-2
fig:16-3
fig:16-4

	\feynmandiagram[inline=(b),horizontal=a to b,red]{
	a [particle=$a$] -- b [particle=$b$] -- {c [particle=$c$], d [particle=$d$]},
	};
	\feynmandiagram[inline=(b),horizontal'=a to b,blue]{
	a [particle=$a$] -- b [particle=$b$] -- {c [particle=$c$], d [particle=$d$]},
	};
	\feynmandiagram[inline=(b),vertical=a to b,green!40!black]{
	a [particle=$a$] -- b [particle=$b$] -- {c [particle=$c$], d [particle=$d$]},
	};
	\feynmandiagram[inline=(b),vertical'=a to b,black]{
	a [particle=$a$] -- b [particle=$b$] -- {c [particle=$c$], d [particle=$d$]},
	};

fig:17-1
fig:17-2
fig:17-3

	\tikzfeynmanset{every diagram={red}}
	\feynmandiagram[small,horizontal=a to b]{
	i1 -- [fermion] a -- [fermion] i2,
	a -- [boson] b,
	};
	\tikzfeynmanset{every diagram={green}}
	\feynmandiagram[medium,horizontal=a to b]{
	i1 -- [fermion] a -- [fermion] i2,
	a -- [boson] b,
	};
	\tikzfeynmanset{every diagram={blue}}
	\feynmandiagram[large,horizontal=a to b]{
	i1 -- [fermion] a -- [fermion] i2,
	a -- [boson] b,
	};

fig:18-1
fig:18-2
fig:18-3
fig:18-4

	\feynmandiagram[nodes=circle,small,horizontal=c to d]{
	{a, b} -- c -- d -- {e, f},
	};
	\feynmandiagram[nodes=circle,small,horizontal=c to d,spring electrical layout]{
	{a, b [electric charge=2]} -- c -- d -- {e, f [electric charge=0.1]},
	};
	\feynmandiagram[nodes=circle,small,horizontal=a to b,layered layout]{
	a -- b -- {c -- {c1, c2}, d -- {d1, d2}},
	{[same layer] c1, d}
	};
	\feynmandiagram[nodes=circle,small,horizontal=a to b,tree layout]{
	a -- b -- {c, d -- {e, f}}
	};

fig:19

	\tikzfeynmanset{
	every vertex={red,dot},
	every particle={blue},
	every blob={draw=green!40!black, pattern color=green!40!black},
	}
	\feynmandiagram[horizontal=a to b]{
	a [particle={$\gamma, Z$}] -- [boson] b [blob],
	c -- [fermion] b -- [fermion] d,
	};

fig:20-1
fig:20-2
fig:20-3
fig:20-4
fig:20-5

	\feynmandiagram[small]{
	a -- b [dot] -- {c, d},
	};
	\feynmandiagram[small]{
	a -- b [square dot] -- {c, d},
	};
	\feynmandiagram[small]{
	a -- b [empty dot] -- {c, d},
	};
	\feynmandiagram[small]{
	a -- b [crossed dot] -- {c, d},
	};
	\feynmandiagram[small]{
	a -- b [blob] -- {c, d}
	};

fig:21

	\tikzfeynmanset{
	every edge={green},
	every boson={red},
	every photon={blue},
	}
	\feynmandiagram[nodes=circle,small]{
	a -- [boson] o -- [photon] b,
	c -- [fermion] o --[scalar] d,
	};

# 其他例子

可以将 PDF 转换成 svg、eps 等矢量图^[4]或者 png 位图^[5]^[6]^[7]

TeX Live 和 MiKTeX 默认集成 Poppler（pdfcrop 和 pdftocairo 就包含其中）

pdfcrop main.pdf && pdftocairo -svg main-crop.pdf # pdf 裁边并转换成 svg

pdf2svg main.pdf main.svg

在以下例子中，使用 standalone 文档类

lualatex -interaction=nonstopmode -shell-escape main.tex

编译出 PDF 文件后自动裁边并转换成 svg 矢量图。

电子 - 正电子湮灭

电子-正电子湮灭

$e^{-}+e^{+}\rightarrow\gamma+\gamma$

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	% pdf2svg \infile\space \outfile
	pdfcrop \infile\space \infile && pdftocairo -svg \infile % 不喜欢用 pdf2svg
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\feynmandiagram[horizontal=f2 to f3]{
	f1 [particle=$e^{-}$] -- [fermion] f2,
	f2 -- [photon] p1 [particle=$\gamma$],
	f2 -- [fermion] f3,
	f3 -- [photon] p2 [particle=$\gamma$],
	f3 -- [fermion] f4 [particle=$e^{+}$],
	};
	\end{document}

Rosenbluth formula

Rosenbluth formula

		lualatex -interaction=nonstopmode -shell-escape main.tex
		pdfcrop main.pdf main.pdf && pdftocairo -svg main.pdf

	\documentclass{article}
	\usepackage{amsmath,amssymb}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\pagestyle{empty}
	\begin{equation}
	\tikzfeynmanset{
	every vertex={red},
	every particle={blue},
	every blob={draw=green!40!black, pattern color=green!40!black},
	}
	\feynmandiagram[inline=(c.base), horizontal=o to c]{
	a -- [fermion, edge label=$p$] o [blob],
	o -- [fermion, edge label=$p^{\prime}$] b,
	c --[boson,momentum={[arrow style=red]$q$}] o,
	};
	\;=\bar{u}(p^{\prime})\left[\gamma^{\mu}F_1(q^{2})+\frac{i\sigma^{\mu\nu}q_{\nu}}{2m}F_2(q^{2})\right]u(p)\notag
	\end{equation}
	\end{document}

顶点(vertex)规则(rule)

顶点规则

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\feynmandiagram[horizontal=a to b]{
	a [particle=$Z$] -- [photon, momentum=$p_{1}$] b,
	f1 [particle=$\overline f$]
	-- [fermion, rmomentum'=$p_{3}$] b
	-- [fermion, momentum=$p_{2}$] f2 [particle=$f$],
	};
	\end{document}

树状(tree-level)图(diagrams)

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\feynmandiagram[horizontal=a to b]{
	i1 [particle=$e^{-}$] -- [fermion] a -- [fermion] i2 [particle=$e^{+}$],
	a -- [photon, edge label=$\gamma$] b,
	f1 [particle=$\mu^{-}$] -- [fermion] b -- [fermion] f2 [particle=$\mu^{+}$],
	};
	\end{document}

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\feynmandiagram[vertical'=a to b]{
	i1 [particle=$e^{-}$]
	-- [fermion] a
	-- [fermion] f1 [particle=$e^{-}$],
	a -- [photon, edge label=$\gamma$] b,
	i2 [particle=$e^{+}$]
	-- [anti fermion] b
	-- [anti fermion] f2 [particle=$e^{+}$],
	};
	\end{document}

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\begin{tikzpicture}
	\begin{feynman}
	\diagram[vertical'=a to b]{
	i1 [particle=$e^{-}$]
	-- [fermion] a
	-- [draw=none] f1 [particle=$e^{+}$],
	a -- [photon, edge label'=$p$] b,
	i2 [particle=$e^{+}$]
	-- [anti fermion] b
	-- [draw=none] f2 [particle=$e^{-}$],
	};
	\diagram*{
	(a) -- [fermion] (f2),
	(b) -- [anti fermion] (f1),
	};
	\end{feynman}
	\end{tikzpicture}
	\end{document}

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\feynmandiagram[layered layout,horizontal=a to b]{
	a -- [boson, edge label=$J/\Psi$] b
	-- [plain, very thick, edge label=$N^{*}$] c
	-- [fermion] d [particle=$\Lambda$],
	b -- [fermion] f1 [particle=$\bar{p}$],
	c -- [charged scalar] f2 [particle=$K^{+}$],
	};
	\end{document}

循环(loops)

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\feynmandiagram[layered layout, horizontal=b to c]{
	a -- [photon, momentum=$p$] b
	-- [fermion, half left, momentum=$k$] c
	-- [fermion, half left, momentum=$k-p$] b,
	c -- [photon, momentum=$p$] d,
	};
	\end{document}

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\feynmandiagram[layered layout, horizontal=b to c]{
	a -- [photon, momentum=$p$] b
	-- [fermion, half left, momentum=$k$] c
	-- [fermion, half left, momentum=$k-p$] b,
	c -- [photon, momentum=$p$] d,
	};
	\end{document}

箱形(box)图(diagrams)

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\feynmandiagram[layered layout, horizontal=a to b]{
	% 画顶部和底部线
	i1 [particle=$d$]
	-- [fermion] a
	-- [photon, edge label=$W^{-}$] b
	-- [fermion] f1 [particle=$\mu^{-}$],
	i2 [particle=$\overline s$]
	-- [anti fermion] c
	-- [photon, edge label'=$W^{+}$] d
	-- [anti fermion] f2 [particle=$\mu^{+}$],
	% 绘制两条内部费米子线
	{ [same layer] a -- [fermion, edge label'=$q$] c },
	{ [same layer] b -- [anti fermion, edge label=$\nu_{\mu}$] d},
	};
	\end{document}

介子(meson)衰变(decay)和(and)混合(mixing)

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\begin{tikzpicture}
	\begin{feynman}
	\vertex (a1) {$\overline b$};
	\vertex[right=1.5cm of a1] (a2);
	\vertex[right=1cm of a2] (a3);
	\vertex[right=1.5cm of a3] (a4) {$\overline u$};

	\vertex[below=2em of a1] (b1) {$d$};
	\vertex[below=2em of a4] (b2) {$d$};

	%% 看第 13.5 节 PGF/TikZ 手册
	\vertex at ($(a2)!0.5!(a3)!0.5cm!90:(a3)$) (d);
	%% 获得 (d) 的等效方法：
	% \vertex at ($(b2)!0.5!(b3) + (0, -0.5cm)$) (d);
	\vertex[above=of a4] (c1) {$u$};
	\vertex[above=2em of c1] (c3) {$\overline d$};
	\vertex at ($(c1)!0.5!(c3) - (1cm, 0)$) (c2);

	\diagram*{
	(a4) -- [fermion] (a3) -- [fermion] (a2) -- [fermion] (a1),
	(b1) -- [fermion] (b2),
	(c3) -- [fermion, out=180, in=45] (c2) -- [fermion, out=-45, in=180] (c1),
	(a2) -- [boson, quarter left] (d) -- [boson, quarter left] (a3),
	(d) -- [boson, bend left, edge label=$W^{+}$] (c2),
	};

	\draw[decoration={brace}, decorate] (b1.south west) -- (a1.north west)
	node [pos=0.5, left] {$B^{0}$};
	\draw[decoration={brace}, decorate] (c3.north east) -- (c1.south east)
	node [pos=0.5, right] {$\pi^{+}$};
	\draw[decoration={brace}, decorate] (a4.north east) -- (b2.south east)
	node [pos=0.5, right] {$\pi^{-}$};
	\end{feynman}
	\end{tikzpicture}
	\end{document}

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\begin{tikzpicture}
	\begin{feynman}
	\vertex (a1) {$\overline b$};
	\vertex[right=1cm of a1] (a2);
	\vertex[right=1cm of a2] (a3);
	\vertex[right=1cm of a3] (a4) {$b$};
	\vertex[right=1cm of a4] (a5);
	\vertex[right=2cm of a5] (a6) {$u$};

	\vertex[below=2em of a1] (b1) {$d$};
	\vertex[right=1cm of b1] (b2);
	\vertex[right=1cm of b2] (b3);
	\vertex[right=1cm of b3] (b4) {$\overline d$};
	\vertex[below=2em of a6] (b5) {$\overline d$};

	\vertex[above=of a6] (c1) {$\overline u$};
	\vertex[above=2em of c1] (c3) {$d$};
	\vertex at ($(c1)!0.5!(c3) - (1cm, 0)$) (c2);

	\diagram*{
	{[edges=fermion]
	(b1) -- (b2) -- (a2) -- (a1),
	(b5) -- (b4) -- (b3) -- (a3) -- (a4) -- (a5) -- (a6),
	},
	(a2) -- [boson, edge label=$W$] (a3),
	(b2) -- [boson, edge label'=$W$] (b3),

	(c1) -- [fermion, out=180, in=-45] (c2) -- [fermion, out=45, in=180] (c3),
	(a5) -- [boson, bend left, edge label=$W^{-}$] (c2),
	};
	\draw[decoration={brace}, decorate] (b1.south west) -- (a1.north west)
	node [pos=0.5, left] {$B^{0}$};
	\draw[decoration={brace}, decorate] (c3.north east) -- (c1.south east)
	node [pos=0.5, right] {$\pi^{-}$};
	\draw[decoration={brace}, decorate] (a6.north east) -- (b5.south east)
	node [pos=0.5, right] {$\pi^{+}$};
	\end{feynman}
	\end{tikzpicture}
	\end{document}

	\documentclass[margin=5pt, convert, convert={outext=.svg, command=\unexpanded{
	pdfcrop \infile\space \infile && pdftocairo -svg \infile
	}}]{standalone}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\begin{tikzpicture}
	\begin{feynman}
	\vertex (a1) {$\overline b$};
	\vertex[right=2cm of a1] (a2);
	\vertex[right=0.5cm of a2] (a3);
	\vertex[right=0.5cm of a3] (a4);
	\vertex[right=2cm of a4] (a5) {$\overline s$};

	\vertex[below=2cm of a1] (b1) {$d$};
	\vertex[below=2cm of a5] (b2) {$d$};

	\vertex[below=1.5em of a5] (c1) {$s$};
	\vertex[above=1.5em of b2] (c3) {$\overline s$};
	\vertex at ($(c1)!0.5!(c3) - (1cm, 0)$) (c2);

	\diagram*{
	{[edges=fermion]
	(a5) -- (a4) -- (a3) -- (a2) -- (a1),
	},
	(b1) -- [fermion] (b2),
	(c3) -- [fermion, out=180, in=-60] (c2) -- [fermion, out=60, in=180] (c1),
	(a3) -- [gluon, bend right] (c2),
	(a4) -- [boson, out=90, in=90, looseness=2.0, edge label'=$W^{+}$] (a2)
	};

	\draw[decoration={brace}, decorate] (b1.south west) -- (a1.north west)
	node [pos=0.5, left] {$B^{0}$};
	\draw[decoration={brace}, decorate] (a5.north east) -- (c1.south east)
	node [pos=0.5, right] {$\phi$};
	\draw[decoration={brace}, decorate] (c3.north east) -- (b2.south east)
	node [pos=0.5, right] {$K^{0}$};
	\end{feynman}
	\end{tikzpicture}
	\end{document}

三个 gluon 的 interaction vertex

	\documentclass{article}
	\usepackage{amsmath,amssymb}
	\usepackage[compat=1.1.0]{tikz-feynman}
	\begin{document}
	\pagestyle{empty}
	\begin{equation}
	\feynmandiagram[inline=(a.base), horizontal=a to b]{
	a [particle=$\nu;\;b$] -- [gluon, momentum'=$p$] b,
	c [particle=$\mu;\;a$] -- [gluon, momentum'=$k$] b,
	d [particle=$\rho;\;c$] -- [gluon, momentum'=$q$] b,
	};
	\;=gf^{abc}\left[g^{\mu\nu}(k-p)^{\rho}+g^{\nu\rho}(p-q)^{\mu}+g^{\rho\mu}(q-k)^{\nu}\right]\notag
	\end{equation}
	\end{document}

# 参考资料

# 配置环境

# 示例

# 线的类型

# 其他例子

# 参考资料

第一章 量子力学诞生

第二章 一维势场中的粒子运动

第一章量子力学诞生

第二章一维势场中的粒子运动