Feynman diagrams inside equation environment

Question

I need to type the expression below I am thinking of using tikzpicture inside the eqnarray environment. Although I am not quite sure which way would be the best to get this done. Can someone please give some feedback on this? Thanks!

Answer 1

For these simple diagrams the tikz-feynman package might be a bit overkill.

You only have three types of diagrams with a variance of nodes:

• . no node,
• o white with border,
• * filled and, maybe,
• + for the diamond shaped at the bottom of the loop.

All three have possibily one label at always the same place.

With a few styles these can achieved with plain TikZ.

amsmath's \text macro helps scale font-sizes in superscripts, this avoids implementing our own \mathchoicer as long as we define lengths in terms of font dependent units (em and ex, see the definition of every diagram).

The third argment (i.e. the second mandatory one) in each command is the content of the label.
The second one describes the list of nodes. For the line diagram these need to contain two tokens, for the loop three and for the cross five. They describe the nodes from left to right from top to bottom.

That means that

\tfCross{.+o*o}{X}

leads to

Code

\documentclass[varwidth]{standalone}
\usepackage{mathtools}
\DeclarePairedDelimiter\p()
\DeclarePairedDelimiter\brak[]
\usepackage{tikz}
\tikzset{
  feynman/.cd,
  every diagram/.style={x=+1.3em, y=+1.3em, baseline=+-.5ex},
  label/.style={anchor=north west,inner sep=+.2em, scale=.707,
    node font=\everymath\expandafter{\the\everymath\scriptstyle}},
  node/.style={shape=circle, inner sep=+0pt, minimum size=+2pt, node contents=},
  node ./.style={feynman/node, shape=coordinate},
  node o/.style={feynman/node, fill=white, draw},
  node */.style={feynman/node, fill,       draw},
  node +/.style={
    feynman/node, fill, draw, shape=rectangle, rotate=45, minimum size=+1pt},
  loop/.style n args={4}{insert path={
      (0,0) node[feynman/label]{$#4$} node[feynman/node #1] -- ++(right:1)
      arc[start angle=-90, delta angle=360, radius=.5] node[feynman/node #2]
      -- ++(right:1) node[feynman/node #3]}},
  cross diagram/.style={
    /tikz/feynman/label/.append style={anchor=south east, inner sep=+.2pt}},
  cross/.style n args={6}{insert path={
    (225:.707) node[feynman/label]{$#6$} node[feynman/node #4]
    -- (45:.707) node[midway,feynman/node #3] node[feynman/node #2]
    (135:.707) node[feynman/node #1] -- (-45:.707) node[feynman/node #5]}},
  line/.style n args={3}{insert path={
    (0,0) node[feynman/label]{$#3$} node[feynman/node #1]
    -- (right:.8) node[feynman/node #2]}}}
\newcommand*\tfInt[4]{%
  \text{\tikz[feynman/every diagram,feynman/#1 diagram/.try,#2]
    \draw[feynman/#1={#3{#4}}];}}
\newcommand*\tfLoop[1][]{\tfInt{loop}{#1}}
\newcommand*\tfCross[1][]{\tfInt{cross}{#1}}
\newcommand*\tfLine[1][]{\tfInt{line}{#1}}
\begin{document}
\begin{multline}
\frac{\hbar}{i} \frac{\delta}{\delta J(x_1)} W\brak J
 = \frac{\hbar}{i} \frac{\delta}{\delta J(x_1)}
     \brak[\bigg]{1+\frac{g}{4!}
       \p[\bigg] { 6             \,\tfLoop{o+o}{x_1} +     \tfCross{oo*oo}{} }}
     e^{\frac 12 \tfLine{oo}{}} \\
 = \brak[\bigg]{
     \frac{g}{4!}
       \p[\bigg] {     6 \cdot 2 \,\tfLoop{.+o}{x_1} + 4 \,\tfCross{oo*.o}{x_1}}
     + \p[\bigg] {1 + \frac{g}{4!}
                     \p[\bigg]{6 \,\tfLoop{o+o}{x_1} +     \tfCross{oo*oo}{}}}
     \tfLine{.*}{x_1}
    } e^{\frac 12 \tfLine{oo}{}} \\
 = \brak[\bigg]{
     \tfLine{.o}{x_1} + \frac{g}{4!} \p[\bigg]{
       12 \,\tfLoop{.+o}{x_1} + 4 \,\tfCross{oo*.o}{x_1}
      + 6 \,\tfLoop{o+o}{} \, \tfLine{.*}{x_1}
      + \tfCross{oo*oo}{} \, \tfLine{.*}{x_1}
     }
   } e^{\frac 12 \tfLine{oo}{}}
\end{multline}
\end{document}

Output