Time oriented wick contractions

Question

I've used simple-wick and simpler-wick but in neither of them I can put arrows in the lines conecting the elements of the contractions.

Does anybody know how to do that?

I can do something with tikz and Xelatex, but I cannot figure it out how to make it work with math symbols.

\documentclass{article}
\usepackage{tikz,bm}
\newcommand\C[1]{\tikz[remember picture]{\node(#1)[inner sep=0pt] 
{\sffamily#1};}}
\usepackage{tikz}
\usepackage{refcount}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{calc}
\begin{document}

\tikzset{->-/.style={decoration={
 markings,
 mark=at position .5 with {\arrow{>}}},postaction={decorate}}}

\tikzset{-<-/.style={decoration={
 markings,
 mark=at position .5 with {\arrow{<}}},postaction={decorate}}}




\begin{equation}
\begin{tabular}{@{}*7{c@{}}}
\C{a}&\C{B}&\C{C}& $\bm\sim$ &\C{X}&\C{Y}&\C{Z}  
\end{tabular}
\mathord{
\begin{tikzpicture}[overlay,remember picture,>=latex,shorten >=1pt,shorten 
<=1pt,very thin]
\draw[->-] (a) --++(0,10pt) -| (X);
\draw[-<-] (B) --++(0,14pt) -| (Y);
\draw[-<-] (C) --++(0,-14pt) -| (Z);
\end{tikzpicture}
 }
\end{equation}

\end{document}

Which gives me something like

Answer 1

Welcome to TeX.SE! A very simpleminded proposal is to just slightly change one definition of the simpler-wick package.

\documentclass{article}
\usepackage{simpler-wick}
\newif\ifWickArrow
\WickArrowfalse
\pgfkeys{
  /simplerwick/.cd,
  arrow/.code={\WickArrowtrue},
  no arrow/.code={\WickArrowfalse}
}

\makeatletter
\def\swick@end#1#2{
  \swick@setfalse@#1
  \tikzexternaldisable
  \begin{tikzpicture}[remember picture, baseline=(swick-close#1.base)]
    \node[use as bounding box, inner sep=0pt, outer sep=0pt] (swick-close#1) {$\displaystyle #2$};
  \end{tikzpicture}
  \tikz[remember picture, overlay]
{\ifWickArrow  
    \draw[-latex] ($(swick-open#1.north) + (0, 3pt)$) 
          -- ($(swick-open#1.base) + (0, \swick@offset) + #1*(0, \swick@sep)$) 
          -- ($(swick-close#1.base) + (0, \swick@offset) + #1*(0, \swick@sep)$) 
          -- ($(swick-close#1.north) + (0, 1pt)$);
\else         
    \draw ($(swick-open#1.north) + (0, 3pt)$) 
          -- ($(swick-open#1.base) + (0, \swick@offset) + #1*(0, \swick@sep)$) 
          -- ($(swick-close#1.base) + (0, \swick@offset) + #1*(0, \swick@sep)$) 
          -- ($(swick-close#1.north) + (0, 3pt)$);
\fi}
  \tikzexternalenable}
\makeatother
\begin{document}
\begin{equation}
  \wick[arrow]{\c\phi A \c\phi}
\end{equation}
\begin{equation}
  \wick{\c\phi A \c\phi}
\end{equation}
\end{document}

As you see, \wick now accepts an option arrow that makes it draw an arrow. This is a minimal surgery, which does not allow you to combine contractions with and without arrows in the same equation. It might be possible to extend this surgery to allow this also, but that won't be minimal any more. Therefore, I'd like to ask you whether or not such mixed cases are needed.

ADDENDUM: A quick modification that allows you to draw the contractions below, and to put the arrow in the middle. This version comes with a list of arrows that is to be passed to \wick. The first entry defines the arrows for all contractions of type \c1, the second is for \c2 and so on.

\documentclass{article}
\usepackage{simpler-wick}
\usetikzlibrary{decorations.markings}
% from https://tex.stackexchange.com/a/39282/121799
\tikzset{W->-/.style={decoration={
  markings,
  mark=at position 0.5*\pgfdecoratedpathlength+2pt with
  {\draw[-latex] (-2pt,0pt) -- (1pt,0pt);}},postaction={decorate}},
  W-<-/.style={decoration={
  markings,
  mark=at position 0.5*\pgfdecoratedpathlength with
  {\draw[latex-] (-2pt,0pt) -- (1pt,0pt);}},postaction={decorate}}
  }
\newif\ifWickBelow
\WickBelowfalse
\pgfkeys{
  /simplerwick/.cd,
  arrows/.store in=\LstWickArrows,
  arrows={-,-,-,-,-,-,-,-,-},
  arrows/.initial={-,-,-,-,-,-,-,-,-}, % the # of contractions is bounded by 9
  below/.code={\WickBelowtrue},
}

\makeatletter
\def\swick@end#1#2{
  \swick@setfalse@#1
  \tikzexternaldisable
  \begin{tikzpicture}[remember picture, baseline=(swick-close#1.base)]
    \node[use as bounding box, inner sep=0pt, outer sep=0pt] (swick-close#1) {$\displaystyle #2$};
  \end{tikzpicture}
  \tikz[remember picture, overlay]
{
\foreach \W@X[count=\W@C] in \LstWickArrows
{\ifnum\W@C=#1
\xdef\myW@style{\W@X}
\fi}
\ifWickBelow
    \draw[\myW@style] ($(swick-open#1.south) + (0, -3pt)$) 
          -- ($(swick-open#1.base) + (0, -\swick@offset) + #1*(0, -\swick@sep)$) 
          -- ($(swick-close#1.base) + (0, -\swick@offset) + #1*(0, -\swick@sep)$) 
          -- ($(swick-close#1.south) + (0, -3pt)$);
\else
    \draw[\myW@style] ($(swick-open#1.north) + (0, 3pt)$) 
          -- ($(swick-open#1.base) + (0, \swick@offset) + #1*(0, \swick@sep)$) 
          -- ($(swick-close#1.base) + (0, \swick@offset) + #1*(0, \swick@sep)$) 
          -- ($(swick-close#1.north) + (0, 3pt)$);
\fi}
  \tikzexternalenable}
\makeatother
\begin{document}
\begin{enumerate}
\item You can specify single arrows like \texttt{W->-} or \texttt{W-<-}: $\displaystyle
  \wick[arrows={-,W->-,W-<-}]{
    \c1 a \c2 b \c3 c \c1 a d \c1 e
    \c1 e \c1 a \c2 b \c3 c \c1 a
  }
$
\item The default is not to draw arrows: $\displaystyle
  \wick{
    \c1 a \c2 b \c3 c \c1 a d \c1 e
    \c1 e \c1 a \c2 b \c3 c \c1 a
  }
$
\item \texttt{below} allows you to draw the contraction below the
equation: $\displaystyle
  \wick[arrows={-,W->-,W-<-},below]{
    \c1 a \c2 b \c3 c \c1 a d \c1 e
    \c1 e \c1 a \c2 b \c3 c \c1 a
  }$
\item Another example: $\displaystyle
  \wick[arrows={W->-,W-<-,-},below]{
    \c1 a \c2 b \c3 c \c1 a d \c1 e
    \c1 e \c1 a \c2 b \c3 c \c1 a
  }$
\item The ordinary keys work as well, e.g.\ to put arrows at the ends: $\displaystyle
  \wick[arrows={latex-,-latex,-},below]{
    \c1 a \c2 b \c3 c \c1 a d \c1 e
    \c1 e \c1 a \c2 b \c3 c \c1 a
  }$
\bigskip
\item Sometimes you may want to add vertical space by hand: $\displaystyle
  \wick[arrows={stealth-,-latex,-}]{
    \c1 a \c2 b \c3 c \c1 a d \c1 e
    \c1 e \c1 a \c2 b \c3 c \c1 a
  }$
\end{enumerate}
\end{document}

As you already see here, you may want to add vertical space. This is because the contractions are drawn as overlays. Note also that one may make the package a bit more powerful once the new version of tikzmark is on CTAN.