path: root/Master/texmf-dist/source/fonts/feyn/feyn.dtx

% \iffalse
% This is feyn.dtx, which manages the use of the feyn Metafont
%
%% This software is copyright 1991, 1994, 2001-2, 2005, 2008-17, Norman Gray.
%% It is distributed under the terms of the 2-clause BSD Licence;
%% see the file LICENCE for details.
%
%<+package|driver>%% VCS Info: Mercurial revision 3e70c259dcfe, 2022-07-18 22:14 +0100, tag 0.4.2 + 0
%<+package>\NeedsTeXFormat{LaTeX2e}
%<+package>\ProvidesPackage{feyn}[2022/07/18 0.4.2]
%<+package>\typeout{Package: `feyn' 0.4.2 <2022/07/18>}
%
%<*driver>
\documentclass{ltxdoc}
\usepackage{feyn}
\title{The feyn font}
\author{Norman Gray\\(\texttt{https://nxg.me.uk})}
\date{Version 0.4.2, 2022 July 18}
\newcommand\Lopt[1]{\textsf {#1}}
\newcommand\file[1]{\texttt {#1}}
\newcommand\Lcount[1]{\textsl {\small#1}}
\newcommand\pstyle[1]{\textsl {#1}}
%% \url macro (url.sty does this better)
\def\setpathdots{\discretionary{.}{}{.}}
\def\setpathslash{\discretionary{/}{}{/}}
{\catcode`\.=\active
 \catcode`\/=\active
  \gdef\pathcats{%
    \catcode`\%=12      \catcode`\~=12
    \catcode`\.=\active  \let.\setpathdots
    \catcode`\/=\active \let/\setpathslash
    \catcode`\#=12      \catcode`\_=12}%
    }
\def\setpath#1{\ttfamily <\nobreak #1\nobreak>\endgroup}
\def\url{\begingroup\pathcats\setpath}
%\RecordChanges
\OnlyDescription
\parskip=\medskipamount
\parindent=0pt
\begin{document}
\maketitle
\DocInput{feyn.dtx}
\end{document}
%</driver>
%
% \fi
%
%
%
%% \CharacterTable
%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
%
% \CheckSum{680}
%
%
%
%
% \newcommand{\pslash}{p\llap{/\kern-0.3pt}}
% \newcommand{\feynx}{\pstyle{feyn}}
% \newcommand{\metafont}{Metafont}
%
%
%
% This document describes the font \feynx, which can be used to produce relatively
% simple Feynman diagrams within equations in a \LaTeX\ document.  The
% package and font aims to be capable of producing all of the diagrams
% of one- and two-loop QED and QCD, plus $\phi^4$ theory.
%
% The other Feynman diagram package which exists is Thorsten Ohl's
% \textsl{feynmf}/\textsl{feynmp} package.  That
% works by creating \metafont\ or MetaPost figures using a preprocessor.
% It's more general than this package, but is at its best when
% creating relatively large diagrams, for figures.
% In contrast, the present system consists of a carefully-designed font
% with which you can easily write simple diagrams, within equations or within text,
% in a size matching the surrounding text size.
%
% \iftrue
% \textbf{Contents:}
% \def\numberline#1{\space\emph{\S#1}~}
% \def\contentsline#1#2#3{#2,~p#3;}
% \makeatletter \@starttoc{toc} \makeatother
% \fi
%
% \subsection*{Status}
%
% The propagators and vertices which are implemented are those of one-
% and two-loop QED and QCD, plus $\phi^4$ theory, plus a few extras
% which commonly appear in non-figure displays (the practical
% definition of `commonly appear is `which I wanted' or `which
% people asked me for').  I'd be delighted to add others which folk
% feel would be useful, as long as they're still in the rather simple
% scope of the font.
%
% \newpage
% \section{Description}
%
% You use the font by including the package \texttt{feyn.sty}, as in
% \begin{verbatim}
% \usepackage{feyn}
% \end{verbatim}
% If you use the `amsmath' package, you should load that before
% loading the `feyn' package.\footnote{Because of a slight peculiarity
% of the amsmath package, the active~`!' command described below will
% not work properly within amsmath |{align}| or |{align*}|
% environments unless the~`!' is made active globally.  This is done
% by default if the `amsmath' package is loaded first, and not done by
% default otherwise.  If you have to override this behaviour for some
% very arcane reason, then you can force the global or local declaration
% of~`!' using the \Lopt{globalbang} and \Lopt{noglobalbang} options
% to the \texttt{$\backslash$usepackage\{feyn\}} command.}
%
% \makeatletter
% \def\refptcirc{\lower\feyn@maxis \hbox to 0pt{\hss$\circ$\hss}}
% \makeatother
% \begin{table}
% \def\tableskip{\noalign{\smallskip}}
% \halign{$\refptcirc\Feyn{#}$%
%     \hfil\quad & $#$\hfil\quad & # \hfil\qquad && # \cr
% \omit Character & \omit  & Name & Width & Height & Depth \cr
% \noalign{\smallskip\hrule\smallskip}
% f & f &	    fermion$^{\dag}$
%	& 2 & 0 & 0 \cr \tableskip
% fs & fs &   short fermion
%	& 1 & 0 & 0 \cr \tableskip
% fl & fl &   fermion loop$^{\dag\ddag}$
%	& 0 & $2-$ & 0 \cr \tableskip
% flS & flS &  fermion loop (small)$^{\dag\ddag}$
%       & 0 & 1 & 0 \cr \tableskip
% flo & flo &   fermion loop (for $\phi^4$ theory)$^{\dag}$
%       & 0 & 2 & 0 \cr \tableskip
% fu & fu &   upward fermion$^\dag$ (45$^\circ$)
%	& $\sqrt2$ & $\sqrt2$ & 0 \cr \tableskip
% fd & fd &   downward fermion$^\dag$
%	& $\sqrt2$ & $\sqrt2$ & 0 \cr \tableskip
% fv & fv &   vertical fermion$^\dag$
%	& 0 & 2 & 0 \cr \tableskip
% f0 & f0 &   spacer
%	& 2 & 0 & 0 \cr \tableskip
% fs0 & fs0 & short spacer
%	& 1 & 0 & 0 \cr \tableskip
% g & g &	    gluon/photon$^{\dag}$
%	& 2 & 0 & 0 \cr \tableskip
% gl & gl &   gluon loop$^{\dag\ddag}$
%	& 0 & $2-$ & 0 \cr \tableskip
% glB & glB & gluon loop (big)$^{\dag}$
%	& 0 & 2.67 & 0 \cr \tableskip
% glS & glS & gluon loop (small)$^{\dag}$
%	& 0 & 1.33 & 0 \cr \tableskip
% g1\quad g2  & g1, g2  & gluon loop, 1st \& 2nd quadrants$^{\dag}$
%       & 0 & 2 & 0 \cr \tableskip
% g4\quad g3  & g4, g3  & gluon loop, 4th \& 3rd quadrants$^{\dag}$
%       & 0 & 0 & -2 \cr \tableskip
% gu & gu &   upward gluon$^\dag$ (45$^\circ$)
%	& $\sqrt2$ & $\sqrt2$ & 0 \cr \tableskip
% gd & gd &   downward gluon$^\dag$
%	& $\sqrt2$ & $\sqrt2$ & 0 \cr \tableskip
% gv & gv &   vertical gluon$^\dag$
%	& 0 & 2 & 0 \cr \tableskip
% m & m &	    massive fermion$^{\dag}$
%	& 2 & 0 & 0 \cr \tableskip
% ms & ms &   short massive fermion
%	& 1 & 0 & 0 \cr \tableskip
% h & h &	    ghost$^{\dag}$
%	& 2 & 0 & 0 \cr \tableskip
% hs & hs &   short ghost
%	& 1 & 0 & 0 \cr \tableskip
% hu & hu &   upward ghost$^{\dag}$ (45$^\circ$)
%	& $\sqrt2$ & $\sqrt2$ & 0 \cr \tableskip
% hd & hd &   downward ghost$^{\dag}$
%	& $\sqrt2$ & $\sqrt2$ & 0 \cr \tableskip
% hl & hl &   ghost loop$^{\dag\ddag}$
%         & 0 & $2-$ & 0 \cr\tableskip
% x & x &	    counterterm vertex & 0 & $a$ & $-a$ \cr \tableskip
% p & p &	    proper vertex	& - & - & - \cr \tableskip
% P & P &	    proper vertex (variant)	& - & - & - \cr \tableskip
% c & c &	    complete vertex	& - & - & - \cr \tableskip
% a & a &	    arrow$^\dag$	& 0 & 0 & 0 \cr
% }
% \caption{\label{chars} The characters in font \feynx, and their
% reference points, marked with circles.  Characters
% marked~$\dag$ have arrowed variants indicated with~`A' and~`V' suffixes;
% and characters marked~$\ddag$ have an upside-down variant
% indicated with a `u' suffix.  The `u' must come before the `A' or
% `V'. Character `a' has an `arrowed variant' in the sense that `aV'
% produces a backward arrow. A length of `$2-$' indicates a length
% slightly less than two units, for aesthetic reasons.}
% \end{table}
%
% The characters in the font are shown in table~\ref{chars}.
% These are shown in textstyle size, but all characters are also available in
% displaystyle size.
% All of the displaystyle characters are additionally offset vertically
% up to the math axis, which has height~$a$.
% All the dimensions are shown as multiples of the
% length of a module which is the length of the short fermion.
% The~$\circ$ shows the reference point of each character.
% The proper vertex and the complete vertex are specified
% in terms of a `blob-radius' which is about half a module.
% They have a width of 2~radii, and a height and depth of 1~radius.
%
% Each of the characters marked with a~$\dag$ in the table has two
% arrowed variants, so that |\feyn{fA + gV}| produces $\feyn{fA +
% gV}$.  The `A' variants produce arrows pointing rightwards or
% upwards, and the `V' variants arrows pointing leftwards or
% downwards.  The characters marked with a~$\ddag$ also have an
% upside-down variant, thus `flu' is an upside-down variant of the
% fermion loop, and `fluV' an arrowed variant.
%
% Note that the fermion, gluon and ghost half-loop characters are
% slightly shorter than the height you might expect.  These characters
% are deliberately slightly squashed partly because that makes them
% look slightly better (in my opinion!) in a one-loop self-energy
% diagram, but also so that the `gl glu' or `fl flu' loop in a
% two-loop diagram looks better.  The loop formed by the pair of `g1
% g2' is the size you might expect.  See section~\ref{s:examples} below
% for some illustrations of this.
%
% The unnassigned positions in the \feynx\ font are filled
% with an obviously wrong dummy character, so that |$\feyn{A}$|, for example,
% produces $\feyn{fs0Afs0}$.
%
% If you were to print out a font table, you would discover that many
% of the glyphs in the font can be obtained using single
% characters, rather than the ligatures mentioned in the table.  Do
% not be tempted to use this as a shortcut, since the assignment of
% glyphs to character positions may be changed without warning from release to
% release, as long as the ligature maps remain valid.
%
% The file \file{feyn.sty} additionally defines a number of macros,
% described here.
% \begin{description}
% \item[\cs{feyn}] Selects the diagram font.  This must be used
%     within math mode.  \cs{Feyn} selects the text-mode diagram font.
% \item[\cs{momentum}\{ch\}\{text\}] sets the character
%     `ch', which may be a ligature, and puts the given text at the recommended
%     annotation position for that character.  |\momentum[pos]{ch}{text}|
%     is the same, except that the optional argument indicates the
%     position relative to the annotation position.  It must be one of
%     `top', `urt', `lrt', `bot', `llft' or `ulft'.  This is rarely
%     used as such, since the |\feyn| and |\Feyn|
%     commands make~`!' a temporarily active character, and define it
%     to be |\momentum|.  See section~\ref{s:examples} for
%     examples and further discussion.
% \item[\cs{belowl\{\}}] A common pattern in diagrams is to have a pair
%     of incoming or outgoing propagators.  If the lower one of this
%     pair is enclosed within |\belowl{...}|, then it is set so that it
%     occupies zero horizontal space, and moved leftwards and
%     downwards, to fit under the upper of the pair of propagators.
%     The command |\belowr{...}| is the same, except that the argument
%     is moved rightwards.
%     See examples below.
% \item[\cs{Diagram\{\}}] This is for building more complicated diagrams.  It
%     takes one argument, which is like the contents of an \texttt{\{array\}}
%     environment---a series of formulae separated by \&'s and \verb-\\-.  See
%     below for an example.  The result is a box on the math-axis.
% \item[\cs{maxis}] Raises a formula to the math-axis, which is
%     occasionally useful  within in-text equations: eg
%     |$\Feyn{fglf} - \maxis{\Feyn{faf}}$| produces
%     $\Feyn{fglf} - \maxis{\Feyn{faf}}$.
% \item[\cs{vertexlabel\{p\}\{text\}}] Allows you to label a vertex.  If
%     the first parameter~$p$ is~$\wedge$, the~\emph{text} is placed above the
%     point at which the command is given, if it is~\texttt{\_}, it is
%     placed below. For example, |$\feyn{f\vertexlabel^{a}}$| produces
%     $\feyn{f\vertexlabel^{a}}$.  More often used within |\Diagram|
%     than elsewhere.
% \item[\cs{feynstrut\{h\}\{d\}}] For use within an (eqn)array environment, or
%     the like. It modifies the control sequence \verb-\strut- to be a strut of
%     height~$h$ and depth~$d$ modules, which can therefore be used to
%     space the array out.  Note that it modifies |\strut|, rather
%     than being the strut itself.
% \item[\cs{annotate\{x\}\{y\}\{text\}}] Puts the \emph{text}, between dollars,
%     in a zero width box at offset~$(x,y)$ modules from the position of the
%     |\annotate| command (which is generally the first command(s) after
%     entering math-mode).  Because the \emph{text} is in math-mode, anything
%     that is not maths should be in an |\mbox|.  You will probably
%     use this only rarely, as the |\momentum| command supports most
%     of the annotation you will need.
% \end{description}
%
% The \feynx\ font is modular, in the sense that all the
% dimensions are in terms of a module of 10pt, and all sizes given
% below are in units of modules.  As well as 10pt, the font has
% versions for 11pt, 12pt, 18pt and 24pt text, and the most
% appropriate one is selected depending on the text size declared (or
% defaulted) in the |\documentclass| command.  This range of sizes
% seems to be appropriate for the sizes required, but the author would
% welcome comments on this.  The distribution
% contains a sample file using the 18pt \feynx\ font in a
% \texttt{foiltex} document.
%
% You draw a diagram by going into math-mode (between \$\dots\$), and selecting
% the diagrams font by the font-changing command \verb-\feyn{}-
% (exactly as you might use \verb-\mathrm- in math-mode). With a couple of
% exceptions, all the characters are obtained by typing a single
% letter, or a couple of letters which form a ligature, so that the
% letter~$f$ in the diagrams font (\verb-$\feyn{f}$-) produces a
% fermion of length~2 (modules), and~$fs$ produces a short fermion of
% length~1.  As usual in maths mode, space characters are ignored, so
% you can add whitespace as required to make the expressions more
% legible.   Some of the more heavily used characters are available in
% both display size and text size, with the text-size version invoked
% by |\Feyn{...}|, so that |\feyn{fglf}| gives $\feyn{fglf}$ and
% |\Feyn{fglf}| gives $\Feyn{fglf}$.  The displaystyle characters
% are all on the math-axis, the textstyle ones are on the text line.
%
% The display and text sizes of diagrams (that is, as produced by
% |\feyn| and |\Feyn| respectively) are intended to be used
% within equations, and they are sized accordingly.  When diagrams
% have significantly complicated annotation, however, this size can
% look unhelpfully cramped, and it is for this case that there is an
% `extended' set of diagram characters, which are approximately double
% the size, and are available, in |\displaystyle| only, with the
% |\FEYN| and |\DIAGRAM| macros.  These are used exactly like the
% |\feyn| and |\Diagram| macros.  Note
% that the line width, the module used by the (rare) |\annotate| command, and the math
% axis, do not change from the sizes they have for the |\feyn|
% command.  That is, this font is \emph{not} the appropriate one to
% use if you simply want a larger font size -- in that case, simply
% increase the \LaTeX\ font size and the \feynx\ font will change in
% size accordingly.  See below for an example of the use of |\FEYN|.
%
% \subsection{More complicated diagrams}
%
% \newdimen\halftextwidth
% \halftextwidth=\textwidth
%   \advance\halftextwidth by -\tabcolsep
%   \advance\halftextwidth by -\arrayrulewidth
%   \divide\halftextwidth by 2
% \newenvironment{codeexample}
%    {\vskip\medskipamount
%     \def\Becomes{\cr
%                  \noalign{\vrule width \arrayrulewidth \hskip\tabcolsep}}
%     \valign\bgroup
%               \hrule height 0pt depth 0pt width \halftextwidth
%               \hsize=\halftextwidth
%               \vfil ## \vfil \cr}
%    {\crcr\egroup
%     \vskip\medskipamount}
% \newenvironment{examplerhs}{\begin{minipage}[t]{\halftextwidth}}
%                            {\\ \end{minipage}}
%
%
% The \feynx\ font is designed so that simple diagrams are simple to
% produce, and are as far as possible writable as a single line of
% characters.  There are a couple of more complicated diagrams which
% are drawable without too much effort.
%
% A common pattern in diagrams is to have a pair
% of incoming or outgoing propagators.  If the lower one of this
% pair is enclosed within |\belowl{...}|, then it is set so that it
% occupies zero horizontal space, and moved leftwards and
% downwards, to fit under the upper of the pair of propagators.  For
% example the sequence |\feyn{f gu \belowl{fd}}| would put the downward
% fermion directly below the upward gauge boson.  See below for this
% and other examples.
%
% The second way of composing more complicated diagrams is to use the
% |\Diagram| macro.  This allows you to lay out a diagram in an
% array-like environment, each cell of which is set within a
% |\feyn{...}| macro.  On the right is the same diagram drawn with
% lines indicating the boundaries between the cells.
% \begin{codeexample}
% \begin{verbatim}
%   \Diagram{   & x \\
%            fs & gv f & gu \\
%               &      & fd }
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
%   \Diagram{   & x \\
%            fs & gv f & gu \\
%               &      & fd }
%   \qquad\left(\quad
%   \makeatletter
%   \Diagram{          &\vrule x    &\vrule height \feyn@maxis \\
%            \hline fs &\vrule gv f &\vrule height \feyn@module gu \\
%            \hline    &\vrule height 0.7\feyn@module &\vrule fd \\
%            \iffalse \hline    &\vrule height \feyn@module &\vrule\fi
%            }
%   \quad\right)
% $\end{examplerhs}
% \end{codeexample}
%
% The |\Diagram| and |\DIAGRAM| macros take an optional argument of
% either `centre' or `bottom': with `centre', the diagram is centred
% on the math axis, with `bottom' the reference point of the diagram
% is the reference point of the bottom-most row of the array.  The
% default is `centre'.
%
% Before the introduction of the |\belowl| macro in \feynx~v0.4, this
% was the only way to produce this pair of angled propagators one on
% top of the other.  With |\belowl|, however, an alternative way of
% producing this diagram is as shown below.
% \begin{codeexample}
% \begin{verbatim}
% \feyn{fs
%   \Diagram[bottom]{x\\gv}
%   f gu\belowl{fd}}
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \feyn{fs
%   \Diagram[bottom]{x\\gv}
%   f gu\belowl{fd}}
% $\end{examplerhs}
% \end{codeexample}
%
% Diagrams much more complicated than this are probably better dealt
% with using Thorsten Ohl's \textsl{feynmf/feynmp} package.
%
% \section{Examples}
% \label{s:examples}
%
% A simple propagator:
% \begin{codeexample}
% \begin{verbatim}
% \feyn{\vertexlabel^a
%     !{fA}p \vertexlabel^b}
% = \displaystyle
%     \frac{i\delta^{ab}}
%          {\pslash-m_0}}
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
%   \feyn{\vertexlabel^a
%     !{fA}p \vertexlabel^b}
%   = \displaystyle
%     \frac{i\delta^{ab}}{\pslash-m_0}
% $\end{examplerhs}
% \end{codeexample}
%
% The |\Diagram| command lays out its arguments as an array.
% \begin{codeexample}
% \begin{verbatim}
%  \Diagram{\vertexlabel^a \\
%    fd \\
%      & g\vertexlabel_{\mu,c} \\
%    \vertexlabel_b fu\\
%    }
%  = ig\gamma_\mu (T^c)_{ab}
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \Diagram{\vertexlabel^a \\
% 		fd \\
% 		    & g\vertexlabel_{\mu,c} \\
% 		\vertexlabel_b fu\\
% 	    }
%     = ig\gamma_\mu (T^c)_{ab}
% $\end{examplerhs}
% \end{codeexample}
% The |\Diagram| is here necessary only for the vertex labels.
% Without those, it would be as simple as:
% \begin{codeexample}
% \begin{verbatim}
% \feyn{fd \belowl{fu} g
%   = ig\gamma_\mu (T^c)_{ab}}
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \feyn{fd \belowl{fu} g} = ig\gamma_\mu (T^c)_{ab}
% $\end{examplerhs}
% \end{codeexample}
%
% An assortment of two-loop diagrams:
% \begin{codeexample}
% \begin{verbatim}
% \feyn{fs f gl f glu f fs}
% \end{verbatim}
% \Becomes
% $\feyn{fs f gl f glu f fs}$
% \end{codeexample}
% This is a ``short-fermion fermion gluon-loop fermion
% gluon-loop-upsidedown fermion short-fermion''.
%
% We can include vertical gluons:
% \begin{codeexample}
% \begin{verbatim}
% \feyn{ms mA g1 gv g2 ms x f}
% \end{verbatim}
% \Becomes
% $\feyn{ms mA g1 gv g2 ms x f}$
% \end{codeexample}
% Note, in this example, that the gluon loop is formed by a pair of
% `g1 g2' characters.  This is because the `gl' half-loop character is
% deliberately slightly squashed, and wouldn't meet the vertical gluon
% properly.  The half-loop character is squashed (as are
% the fermion and ghost half-loops) partly because it looks
% slightly better in a one-loop self-energy diagram, but also so that
% the `gl glu' two-gluon loop in a two-loop diagram looks better:
% \begin{codeexample}
% \begin{verbatim}
% \Diagram{&gl glu\\
%  fsf g1 f&f g2 ffs \\}
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \Diagram{&gl glu\\
% fsf g1 f&f g2 ffs \\}
% $\end{examplerhs}
% \end{codeexample}
% The diagrams for `hl hlu' or `flA fluV', for example, are very similar.
%
% The |\momentum| command (more usually called with simply the~`!'
% character) allows you to annotate a propagator with a momentum or a
% particle label.  For example
% \begin{codeexample}
% \begin{verbatim}
% \feyn{fA + !{fA}{p} + ![bot]{fA}{p}}
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \feyn{fA + !{fA}{p} + ![bot]{fA}{p}}
% $\end{examplerhs}
% \end{codeexample}
%
% \begin{codeexample}
% \begin{verbatim}
% \feyn{f !{g1A}1 !{g2V}2
%   !{g3A}3 !{g4V}4 f},
% \feyn{fs f !{flA}{p}
%       !{fluV}{k} f fs}
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \feyn{f !{g1A}1 !{g2V}2
%   !{g3A}3 !{g4V}4 f},
% \feyn{fs f !{flA}{p}
%       !{fluV}{k} f fs}
% $\end{examplerhs}
% \end{codeexample}
%
% \begin{codeexample}
% \begin{verbatim}
% \feyn{!{fA}p
%    f!{glBV}k !{glSA}l
%    a\vertexlabel_{p+k-l} ff}
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \feyn{!{fA}p
%    f!{glBV}k !{glSA}l
%    a\vertexlabel_{p+k-l} ff}
% $\end{examplerhs}
% \end{codeexample}
%
% \newenvironment{bigdisplay}[1]
%    {\endgraf
%     \penalty 50 \vskip 0.5\baselineskip plus 0.5\textheight
%     \vbox\bgroup
%     #1\endgraf \smallskip
%     \vbox{\hrule\hbox to \textwidth{\vrule height 1.5ex\hfil\vrule}}%
%     \parskip0pt}
%    {\vbox{\hbox to \textwidth{\vrule height 1.5ex \hfil\vrule}\hrule}
%     \egroup}
%
% \begin{bigdisplay}{Bremsstrahlung:}
% \begin{verbatim}
% \[
%   \Diagram{        & x \\
%                    & ![ulft]{gvV}{q=p'+k-p} & !{guA}k \\
%        ![bot]{fA}p & ![bot]{fA}{p'+k}       & ![lrt]{fA}{p'} \\
%         }
%         +
%   \Diagram{    & !{guA}k \\
%         !{fA}p & ![bot]{fA}{p-k} fs & !{fA}{p'} \\
%                &                    & ![lrt]{gvA}{q=p'+k-p} \\
%                &                    & x\\
%         }
% \]
% \end{verbatim}
% \hrule
% \[
%   \Diagram{        & x \\
%                    & ![ulft]{gvV}{q=p'+k-p}   & !{guA}k \\
%            ![bot]{fA}p & ![bot]{fA}{p'+k} & ![lrt]{fA}{p'} \\
%         }
%         +
%   \Diagram{    & !{guA}k \\
%            !{fA}p & ![bot]{fA}{p-k} fs & !{fA}{p'} \\
%                &         & ![lrt]{gvA}{q=p'+k-p} \\
%                &         & x\\
%         }
% \]
% \end{bigdisplay}
%
% \begin{bigdisplay}{And now the same, with
% \texttt{\textbackslash belowl} and \texttt{\textbackslash belowr}:}
% \begin{verbatim}
% \[
% \def\stack#1#2{\Diagram[bottom]{#1\\#2}}
% \feyn{
%   !{fA}p
%     \stack{x}{![ulft]{gvV}{q=p'+k-p}}
%     ![bot]{fA}{p'+k}
%     \stack{!{guA}k}{![lrt]{fA}{p'}}
%   +
%   !{fA}p
%     \belowr{![llft]{gdA}k} !{fA}{p-k}
%     fs
%     \stack x{!{gvV}{q=p'+k-p}} !{fA}{p'}}
% \]
% \end{verbatim}
% \hrule
% \[
% \def\stack#1#2{\Diagram[bottom]{#1\\#2}}
% \feyn{
%   !{fA}p
%     \stack{x}{![ulft]{gvV}{q=p'+k-p}}
%     ![bot]{fA}{p'+k}
%     \stack{!{guA}k}{![lrt]{fA}{p'}}
%   +
%   !{fA}p
%     \belowr{![llft]{gdA}k} !{fA}{p-k}
%     fs
%     \stack x{!{gvV}{q=p'+k-p}} !{fA}{p'}}
% \]
% \end{bigdisplay}
%
% The |\stack| macro isn't defined by the \feynx\ package, but
% it is useful enough that you might want to define it as one of your
% own macros.
%
% \iffalse
% We can also have diagrams in the text, like~$\Feyn{fsfglffs}$, and we can
% annotate the diagrams
% \begin{codeexample}
% \begin{verbatim}
% \annotate{2}{-0.5}
%     {\mbox{counterterm}}
% \feyn{ms m gl ![llft]{gv}l
%       ms x f}
% \end{verbatim}
% \Becomes
% \begin{examplerhs} $
% \annotate{2}{-0.5}
%     {\mbox{counterterm}}
% \feyn{ms m gl ![llft]{gv}l
%       ms x f}
% $\end{examplerhs}
% \end{codeexample}
% This is a ``short-massive massive gluon-loop gluon-vertical
% short-massive counterterm fermion''.
% \fi
%
% \begin{bigdisplay}{The expression for the heavy-fermion self-energy in the \textsc{ope} is:}
% \begin{verbatim}
% \def\bracket#1{\langle #1 \rangle}
% \def\stack#1#2{\Diagram[bottom]{#1\\#2}}
% \begin{eqnarray*}
% -i\Sigma_{\rm ope} &=&
%     \left[ \feyn{faf + fsfglffs + \cdots} \right] 1
%               \feynstrut{1}{1}\strut \\
%     && \quad{}+ \left[ \feyn{ fxfs0glfs0xf + \cdots} \right]
%         \bracket{\overline\psi M \psi} \\
%     && \quad{}+ \left[
%                   \feyn{fs \stack x{gv} fs \stack x{gv} fs} + \cdots
%                 \right]
%         \bracket{G_{\mu\nu}^a G_{\mu\nu}^a}\\
% \end{eqnarray*}
% \end{verbatim}
% \hrule
% \def\bracket#1{\langle #1 \rangle}
% \def\stack#1#2{\Diagram[bottom]{#1\\#2}}
% \begin{eqnarray*}
% -i\Sigma_{\rm ope} &=&
%     \left[ \feyn{faf + fsfglffs + \cdots} \right] 1
%               \feynstrut{1}{1}\strut \\
%     && \quad{}+ \left[ \feyn{ fxfs0glfs0xf + \cdots} \right]
%         \bracket{\overline\psi M \psi} \\
%     && \quad{}+ \left[
%                   \feyn{fs \stack x{gv} fs \stack x{gv} fs} + \cdots
%                 \right]
%         \bracket{G_{\mu\nu}^a G_{\mu\nu}^a}\\
% \end{eqnarray*}
% \end{bigdisplay}
%
% Now for two examples using |\FEYN|:
% \begin{codeexample}
% \begin{verbatim}
% \feyn{f gu \belowl{fd}}
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \feyn{f gu \belowl{fd}}
% $\end{examplerhs}
% \end{codeexample}
% \begin{codeexample}
% \begin{verbatim}
% \FEYN{
%    !{fA}s !{gu}{W^-_\mu}
%      \belowl{!{fdA}u}
% }
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \FEYN{
%    !{fA}s !{gu}{W^-_\mu} \belowl{!{fdA}u}
% }
% $\end{examplerhs}
% \end{codeexample}
% \begin{codeexample}
% \begin{verbatim}
% \DIAGRAM{
%    !{fA}s &!{gu}{W^-_\mu}\\
%           & !{fdA}u
% }
% \end{verbatim}
% \Becomes
% \begin{examplerhs}$
% \DIAGRAM{!{fA}s &!{gu}{W^-_\mu}\\ & !{fdA}u}
% $\end{examplerhs}
% \end{codeexample}
%
% \begin{bigdisplay}{The Feynman Rules are as follows:}
% \begin{verbatim}
% \def\arraystretch{3} \arraycolsep=0.2cm
% \[ \begin{array}{rcl}
% \feyn{\vertexlabel^a !{fA}p \vertexlabel^b} % quark prop
%   &=& \displaystyle
% 	{i\delta^{ab} \over \pslash- m_0} \\
%
% \Diagram{\vertexlabel^a \\ fd \\ & g\vertexlabel_{\mu,c} \\
%    \vertexlabel_b fu\\}  % 3-point vertex
%  &=& \displaystyle
%    ig\gamma_\mu (t^c)_{ab} \\
%
% \feyn{\vertexlabel_{\mu, a} !{gA}k \vertexlabel_{\nu, b}} % gluon prop
% &=& \displaystyle
%   {-i\over k^2} \left[g_{\mu\nu} + (a_0 - 1) {k_\mu k_\nu \over k^2}\right]
%   \delta^{ab} \\
%
% \Diagram{\vertexlabel^{\alpha,a} \\
%          !{gdA}p \\
%                  & !{gA}r \vertexlabel_{\gamma,c} \\
%          !{guA}q \\
%          \vertexlabel_{\beta,b}
%         } % 3-gluon vertex
%     &=& \displaystyle
% 	-g f^{abc} (
% 	g_{\beta\gamma}  (q-r)_\alpha +
% 	g_{\gamma\alpha} (r-p)_\beta +
% 	g_{\alpha\beta}  (p-q)_\gamma
% 	) \\
%
% \feyn{\vertexlabel^a !hp \vertexlabel^b} % ghost prop
% &=& \displaystyle
% 	{i \over p^2} \delta_{ab} \\
%
% \Diagram{\vertexlabel^b \\ hd \\ & g\vertexlabel^{\mu,a} \\
%    \vertexlabel_c hu\\} % ghost-gluon vertex
% &=& \displaystyle
% 	-g f^{abc}p_\mu
% 	\quad\raise 1ex\hbox{\vtop{\hsize=15em
% 	    where $p$ is the momentum of the outgoing positive energy
%           ghost\par}}
% \end{array} \]
% \end{verbatim}
% \end{bigdisplay}
%
% \begin{bigdisplay}{\dots giving:}
% \def\arraystretch{3} \arraycolsep=0.2cm
% \[ \begin{array}{rcl}
%     \feyn{\vertexlabel^a !{fA}p \vertexlabel^b}
%     &=& \displaystyle
% 	{i\delta^{ab} \over \pslash- m_0} \\
%
%     \Diagram{\vertexlabel^a \\ fd \\ & g\vertexlabel_{\mu,c} \\
%          \vertexlabel_b fu\\}
%     &=& \displaystyle
% 	ig\gamma_\mu (t^c)_{ab} \\
%
%     \feyn{\vertexlabel_{\mu, a} !{gA}k \vertexlabel_{\nu, b}}
%     &=& \displaystyle
%     {-i\over k^2} \left[g_{\mu\nu} + (a_0 - 1) {k_\mu k_\nu \over k^2}\right]
%     \delta^{ab} \\
%
% \Diagram{\vertexlabel^{\alpha,a} \\
%          !{gdA}p \\
%                  & !{gA}r \vertexlabel_{\gamma,c} \\
%          !{guA}q \\
%          \vertexlabel_{\beta,b}
%         }
%     &=& \displaystyle
% 	-g f^{abc} (
% 	g_{\beta\gamma}  (q-r)_\alpha +
% 	g_{\gamma\alpha} (r-p)_\beta +
% 	g_{\alpha\beta}  (p-q)_\gamma
% 	) \\
%
%     \feyn{\vertexlabel^a !hp \vertexlabel^b}
%     &=& \displaystyle
% 	{i \over p^2} \delta_{ab} \\
%
%     \Diagram{\vertexlabel^b \\ hd \\ & g\vertexlabel^{\mu,a} \\
% 	\vertexlabel_c hu\\}
%     &=& \displaystyle
% 	-g f^{abc}p_\mu
% 	\quad\raise 1ex\hbox{\vtop{\hsize=15em
% 	    where $p$ is the momentum of the outgoing positive energy
%           ghost\par}}
% \end{array} \]
% \end{bigdisplay}
%
% \begin{bigdisplay}{The diagrams can very naturally appear as parts of equations
% (as is perhaps by now obvious):}
% \begin{verbatim}
% \begin{eqnarray}
% \feyn{fcf} &=& \feyn{faf + fpf + fpfpf + \cdots} \\
%     &=& \sum_{n=0}^\infty \feyn{fsafs ( pfsafs)}^n \\
%     &=& \feyn{\frac{fsafs}{1-(pfsafs)}}.
% \end{eqnarray}
% \end{verbatim}
% \hrule
% \begin{eqnarray}
% \feyn{fcf} &=& \feyn{faf + fpf + fpfpf + \cdots} \\
%     &=& \sum_{n=0}^\infty \feyn{fsafs ( pfsafs)}^n \\
%     &=& \feyn{\frac{fsafs}{1-(pfsafs)}}.
% \end{eqnarray}
% \end{bigdisplay}
%
% \section{Installation}
%
% The nominal distribution point for the Feyn package is CTAN,
% under \texttt{fonts/feyn}\footnote{\url{https://ctan.org/pkg/feyn}}.
%
% The feyn package is included in the TeXLive distribution\footnote{\url{http://www.tug.org/texlive/}}, so
% you may have it on your machine already.  If not, or if you need a
% more up-to-date version, read on.
%
% Since the package is on CTAN, it should be easily installed and
% updated using the tools which support this in your TeX distribution.
% For TeXLive, that's
% `tlmgr'\footnote{\url{https://www.tug.org/texlive/tlmgr.html}}, and
% for MikTeX see the maintenance section of the
% manual\footnote{\url{https://docs.miktex.org/faq/maintenance.html}}.
%
% \subsection{Installing by hand}
%
% If, for some reason, you need to install the package by hand, then
% you should be able to find generic instructions for installing
% \LaTeX\ files at
% \url{http://www.tex.ac.uk/cgi-bin/texfaq2html?label=installthings}.
%
% In brief: If you have not done so already, you need to extract the package
% file from the distribution file using |latex feyn.ins|.  The
% resulting \file{feyn.sty} should be installed in the usual location
% for style files -- that is, something like
% \file{texmf.local/tex/latex/feyn.sty}.  The \metafont\ source files
% \file{*.mf} should be installed in a directory with a location such as
% \file{texmf.local/fonts/source/feyn/}.  That should be all you need
% to do as regards the installation of the fonts -- if your \TeX\
% setup is installed correctly, then the usual font-generation
% commands (such as \file{mktexpk} for example) should work as normal,
% and these will usually be invoked by default when \LaTeX\ or
% pdf\LaTeX\ is run.
%
% If you are using a \TeX\ system based on TeXLive (which is true of most Unix
% installations, and most macOS installations), then you can
% determine the style-file and \metafont\ search paths using the commands
% \begin{verbatim}
% % kpsepath tex
% % kpsepath mf
% \end{verbatim}
% respectively.  After you have installed them, you will probably need
% to give the command \texttt{mktexlsr} to rebuild the paths database,
% and you can confirm that the files are findable with the commands
% \texttt{kpsewhich feyn.sty} and \texttt{kpsewhich feyn10.mf}.
%
% \section{Licence}
%
% The following is the text of the BSD 2-clause licence.
%
% All rights reserved.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are
% met:
%
% 1. Redistributions of source code must retain the above copyright
% notice, this list of conditions and the following disclaimer.
%
% 2. Redistributions in binary form must reproduce the above copyright
% notice, this list of conditions and the following disclaimer in the
% documentation and/or other materials provided with the distribution.
%
% This software is provided by the copyright holders and contributors
% ``as is'' and any express or implied warranties, including, but not
% limited to, the implied warranties of merchantability and fitness for
% a particular purpose are disclaimed. in no event shall the copyright
% holder or contributors be liable for any direct, indirect, incidental,
% special, exemplary, or consequential damages (including, but not
% limited to, procurement of substitute goods or services; loss of use,
% data, or profits; or business interruption) however caused and on any
% theory of liability, whether in contract, strict liability, or tort
% (including negligence or otherwise) arising in any way out of the use
% of this software, even if advised of the possibility of such damage.
%
%
% \subsection*{Acknowledgements}
%
% Thanks to Purnendu Chakraborty, Fabio Correa, Bryan Chen, Hoang
% Nghia Nguyen and Luciano Pandola for
% suggestions and testing (and encouragement) at various times.
%
%
% \StopEventually{}
%
% \section{Implementation}
%    \begin{macrocode}
%<*package>
%    \end{macrocode}
%
% Start off with the available options.
%
% A wrinkle is that the |{align}| environment, which is defined
% in the amsmath package, reads its contents before processing them,
% which means that a `!' within the environment has its catcode fixed
% before it can be changed by |\feyn| or |\diagram|.  To handle this
% situation, we support \Lopt{globalbang} and \Lopt{noglobalbang}
% options, which cause the `!' character to be redefined globally or
% not.  The default depends on whether the amsmath package was loaded
% before this one was.
%    \begin{macrocode}
\newif\ifFeyn@globalbang
\@ifpackageloaded{amsmath}{\Feyn@globalbangtrue}{\Feyn@globalbangfalse}
\DeclareOption{globalbang}{\Feyn@globalbangtrue}
\DeclareOption{noglobalbang}{\Feyn@globalbangfalse}
%    \end{macrocode}
%
% Now process the options specified in the package command.
%    \begin{macrocode}
\ProcessOptions
%    \end{macrocode}
%
% Declare the feyn math font family.  The |\skewchar| for this font
% (see the \TeX book, p431) can be set to zero, since it's a
% completely upright maths font (the least of its peculiarities).  We
% don't have the font in much of a range of sizes.
%    \begin{macrocode}
\DeclareFontFamily{OMS}{feyn}{\skewchar\font'000}
\DeclareFontShape{OMS}{feyn}{m}{n}{%
	<-10.5>feyn10%
	<10.5-11.5>feyn11%
	<11.5-15>feyn12%
        <15-21>feyn18%
        <21->feyn24%
	}{}
%    \end{macrocode}
%
% Now do the same for the text-size fonts, declaring the textfeyn math
% font family.
%    \begin{macrocode}
\DeclareFontFamily{OMS}{textfeyn}{\skewchar\font'000}
\DeclareFontShape{OMS}{textfeyn}{m}{n}{%
	<-10.5>feyntext10%
	<10.5-11.5>feyntext11%
	<11.5-15>feyntext12%
        <15-21>feyntext18%
        <21->feyntext24%
	}{}
%    \end{macrocode}
%
% Finally, do the same for the extended-size fonts, declaring the
% feynx math font family.
%    \begin{macrocode}
\DeclareFontFamily{OMS}{feynx}{\skewchar\font'000}
\DeclareFontShape{OMS}{feynx}{m}{n}{%
	<-10.5>feynx10%
	<10.5-11.5>feynx11%
	<11.5-15>feynx12%
        <15-21>feynx18%
        <21->feynx24%
	}{}
%    \end{macrocode}
%
% XXX It would be nice to arrange things so that superscripts in
% the feyn font were drawn from cmmi7, or something.  The original
% feyn.sty arranged this with |\scriptfont\diagramfam=\ninmi|, but
% it's not clear what the analogue in the FSS is.
%
% Now declare the `feynman' symbol font, and make the command |\feyn|
% set its argument in that font.  Similarly have |\Feyn| invoke the
% feynman symbol font for the text sizes.
%    \begin{macrocode}
\DeclareSymbolFont{feynman}{OMS}{feyn}{m}{n}
\DeclareSymbolFontAlphabet{\feyn@alphabet}{feynman}
\DeclareSymbolFont{textfeynman}{OMS}{textfeyn}{m}{n}
\DeclareSymbolFontAlphabet{\Feyn@alphabet}{textfeynman}
\DeclareSymbolFont{feynmanextended}{OMS}{feynx}{m}{n}
\DeclareSymbolFontAlphabet{\FEYN@alphabet}{feynmanextended}
%    \end{macrocode}
%
% Now use these font-setting commands, defining |\feyn| and |\Feyn| to
% switch to the given alphabets, defining ! as a shortcut for
% |\momentum| (so that |!{x}{y}| is interpreted as |\momentum{x}{y}|).
% We have to make sure that the `!' character produces that character
% everywhere except within |\feyn| or |\Feyn|.  How we do this depends
% on the value of the |\ifFeyn@globalbang| switch.
% \begin{macro}{\feyn}
%    \begin{macrocode}
\ifFeyn@globalbang
  \catcode`\!=\active
  \def!{\char`\!}               % ! produces this character everywhere
  \def\feyn{\begingroup
    \let!\momentum              % ...except within \feyn
    \feyn@}
  \def\Feyn{\begingroup
    \let!\momentum              % ...or \Feyn
    \Feyn@}
  \def\FEYN{\begingroup
    \let!\momentum              % ...or \FEYN
    \FEYN@}
\else
  {\catcode`\!=\active          % only make ! active within \feyn
    \gdef\feyn{%
      \begingroup  % ends in \feyn@
      \catcode`\!=\active
      \let!=\momentum
      \feyn@}
    \gdef\Feyn{%
      \begingroup  % ends in \Feyn@
      \catcode`\!=\active
      \let!=\momentum
      \Feyn@}
    \gdef\FEYN{%
      \begingroup  % ends in \FEYN@
      \catcode`\!=\active
      \let!=\momentum
      \FEYN@}}
\fi
\def\feyn@#1{\let\feyn@mfmodule\feyn@mfbasemodule
  \feyn@alphabet{#1}\endgroup}
\def\Feyn@#1{\let\feyn@mfmodule\feyn@mfbasemodule
  \Feyn@alphabet{#1}\endgroup}
\def\FEYN@#1{\let\feyn@mfmodule\feyn@mfextendedmodule
  \FEYN@alphabet{#1}\endgroup}
%    \end{macrocode}
% \end{macro}
%
%
% Now get the size of the `module' (the length of the fermion), and the
% height of the math-axis, from the font.  You might think that the
% math-axis is obtainable from |\fontdimen22| of the font, but we do
% not load it as an |{operator}| font when we invoke
% |\DeclareSymbolFont|, so it does not have all 22 parameters that a
% symbol font (as the \TeX book uses the term, rather than \LaTeXe's
% NFSS).  I confess I don't \emph{really} understand the ins and outs
% of this, but this route is robust and not wrong.
%
% The character |"20| in the feyn font is a dummy charcter, with width
% |module#| and height |a#| (using the dimensions of the font
% file).  Use this to set the |\feyn@module| and |\feyn@maxis|.  Note
% that the `module' used in this package file is twice the module used
% in the \metafont\ files themselves.
% \begin{macro}{\feyn@module}
% \begin{macro}{\feyn@maxis}
%    \begin{macrocode}
\DeclareMathSymbol{\FeynSpaceChar}{\mathord}{feynman}{"20}
\setbox0=\hbox{$\FeynSpaceChar$}
\newdimen\feyn@mfbasemodule \feyn@mfbasemodule=\wd0
\newdimen\feyn@module   \feyn@module=2\wd0
\newdimen\feyn@maxis    \feyn@maxis=\ht0
\DeclareMathSymbol{\FeynxSpaceChar}{\mathord}{feynmanextended}{"20}
\setbox0=\hbox{$\FeynxSpaceChar$}
\newdimen\feyn@mfextendedmodule \feyn@mfextendedmodule=\wd0
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\Diagram}
% Define the |\Diagram| macro, which lays out a semi-complicated
% diagram in 2-d.  The macro takes an optional argument which can be
% either |[bottom]| or |[centre]|
%    \begin{macrocode}
{\catcode`\!=\active
  \gdef\Diagram{%
    \begingroup  % ends in \Diagram@
    \catcode`\!=\active
    \let!\momentum
    % \Diagram@
    \@ifnextchar[\Diagram@{\Diagram@[centre]}%]
  }}
\let\Diagram@pos@centre\vcenter
\let\Diagram@pos@center\vcenter     %for Webster fans
\let\Diagram@pos@bottom\relax
\def\Diagram@[#1]#2{\setbox0=\hbox{\vbox{\offinterlineskip \let\\\cr
    \halign{&$\displaystyle\feyn{##}$\cr #2\crcr}}}%
%    \end{macrocode}
% At this point, |\box0| has zero depth.  It must be an hbox, because
% we're fiddling with its height within a enclosing |\vbox|.  See the
% \TeX book pp 388--389. This takes advantage of appx G, rule 8 to
% move box0 down by the height of the math axis.  The construction
% |\dp0 = -2\fontdimen22 \textfont2| also works, in the sense of
% moving the box onto the math axis, but makes the box too small,
% which means that surrounding text can encroach.
%    \begin{macrocode}
    \@tempdima=\ht0
    \advance\@tempdima by 2\feyn@maxis \ht0=\@tempdima
    % no error checking -- unrecognised placement specifiers just expand to \relax
    \csname Diagram@pos@#1\endcsname{\box0}%
    \endgroup}% end group begun in \Diagram
%    \end{macrocode}
% \end{macro}
%
% Define |\DIAGRAM| identically, except for using |\FEYN| rather than |\feyn|.
%    \begin{macrocode}
{\catcode`\!=\active
  \gdef\DIAGRAM{%
    \begingroup  % ends in \Diagram@
    \catcode`\!=\active
    \let!\momentum
    % \DIAGRAM@
    \@ifnextchar[\DIAGRAM@{\DIAGRAM@[centre]}%]
  }}
\def\DIAGRAM@[#1]#2{\setbox0=\hbox{\vbox{\offinterlineskip \let\\\cr
    \halign{&$\displaystyle\FEYN{##}$\cr #2\crcr}}}%
    \@tempdima=\ht0
    \advance\@tempdima by 2\feyn@maxis \ht0=\@tempdima
    \csname Diagram@pos@#1\endcsname{\box0}%
    \endgroup}% end group begun in \Diagram
%    \end{macrocode}
%
% \begin{macro}{\maxis}
% Raise the argument to the math axis.
%    \begin{macrocode}
\def\maxis#1{\raise\feyn@maxis \hbox{$#1$}}
%    \end{macrocode}
% \end{macro}
%
% \iffalse
% I feel that something like the following is surely somehow useful,
% but the spacing doesn't quite work out with what I've got here.
% \def\fstack#1{\vbox{\baselineskip=0pt \@fstack#1,,}}
% \def\@fstack#1,{%
%   \def\@tempa{#1}%
%   \ifx\@tempa\@empty
%     \let\@next\relax
%   \else
%     \hbox{$\feyn{#1}$}%
%     \let\@next\@fstack
%   \fi
%   \@next
% }
% \[
%   \feyn{fsfg1\fstack{f0 gl,f0 glu,gv,ff}g2ffs \showlists}
% \]
% \fi
%
% \begin{macro}{\belowl}
% The argument of the |\belowl| macro is a string of characters in the
% \feynx\ font.  They are set in a box, and then moved so that the box
% takes up zero horizontal width, and is moved downwards by its height
% -- that is, it is moved diagonally downwards and leftwards.  It
% means that the bottom half of a pair of incoming or outgoing
% propagators can be set immediately belowl the upper half, without
% having to use the |\Diagram| macro.
%    \begin{macrocode}
\def\belowl#1{%
  \ifdim\feyn@mfmodule=\feyn@mfbasemodule
    \let\@next\feyn
  \else
    \let\@next\FEYN
  \fi
  \setbox0\hbox{$\@next{#1}$}%
  \hskip-\wd0 \lower\ht0\box0
}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\belowr}
% The |\belowr| macro is almost exactly the same, except that the
% argument is shifted rightwards, which is sometimes more natural to
% express.
%    \begin{macrocode}
\def\belowr#1{%
  \ifdim\feyn@mfmodule=\feyn@mfbasemodule
    \let\@next\feyn
  \else
    \let\@next\FEYN
  \fi
  \setbox0\hbox{$\@next{#1}$}%
  \@tempdima=\wd0
  \lower\ht0\box0
  \hskip-\@tempdima
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\momentum}
% Manages annotation of characters.  |\momentum{ch}{text}| sets the character
% ch, which may be a ligature, and puts the given text at the recommended
% annotation position for that character.  |\momentum[pos]{ch}{text}|
% is the same, except that the optional argument indicates the
% position relative to the annotation position.  It must be one of
% `top', `urt', `lrt', `bot', `llft' or `ulft'.
%
% First, some support macros.
%
% |\feyn@nudge| is a small amount
% which is added to the annotation positions, to keep them clear of the
% point they're annotating.
%    \begin{macrocode}
\newdimen\feyn@nudge
  \feyn@nudge=\feyn@mfbasemodule \divide\feyn@nudge by 3
%    \end{macrocode}
%
% The various |\feyn@pos@<x>| macros position their third argument
% adjacent to a point offset by an amount |(#1,#2)| from the current
% position.  The macro |\feyn@pos@top| has the third argument adjacent
% and above the point, |\feyn@pos@urt| has it to the upper-right, and
% so on.
%    \begin{macrocode}
\def\feyn@pos@top#1#2#3{% top
    \leavevmode
    \@tempdima=#2\feyn@mfmodule \advance\@tempdima\feyn@nudge
    \setbox1=\hbox{\raise \@tempdima\hbox to 0pt{%
    \hskip #1\feyn@mfmodule
        \hbox to 0pt{\hss$\scriptstyle #3$\hss}\hss}}%
    \ht1=0pt \dp1=0pt \box1}
\def\feyn@pos@urt#1#2#3{% urt
    \leavevmode
    \@tempdima=#2\feyn@mfmodule \advance\@tempdima\feyn@nudge
    \setbox1=\hbox{\raise \@tempdima\hbox to 0pt{%
        \hskip #1\feyn@mfmodule \hskip\feyn@nudge $\scriptstyle #3$\hss}}%
    \ht1=0pt \dp1=0pt \box1}
\def\feyn@pos@lrt#1#2#3{% lrt
    \leavevmode
    \setbox0=\hbox to 0pt{\hskip\feyn@nudge $\scriptstyle #3$\hss}%
    \@tempdima=#2\feyn@mfmodule
        \advance\@tempdima -\ht0
        \advance\@tempdima-\feyn@nudge
    \setbox1=\hbox{\raise \@tempdima\hbox to 0pt{%
        \hskip #1\feyn@mfmodule \box0\hss}}%
    \ht1=0pt \dp1=0pt \box1}
\def\feyn@pos@bot#1#2#3{% bot
    \leavevmode
    \setbox0=\hbox to 0pt{\hss$\scriptstyle #3$\hss}%
    \@tempdima=#2\feyn@mfmodule
        \advance\@tempdima -\ht0
        \advance\@tempdima-\feyn@nudge
    \setbox1=\hbox{\raise \@tempdima\hbox to 0pt{%
        \hskip #1\feyn@mfmodule \box0\hss}}%
    \ht1=0pt \dp1=0pt \box1}
\def\feyn@pos@llft#1#2#3{% llft
    \leavevmode
    \setbox0=\hbox to 0pt{\hss$\scriptstyle #3$\hskip\feyn@nudge}%
    \@tempdima=#2\feyn@mfmodule
        \advance\@tempdima -\ht0
        \advance\@tempdima-\feyn@nudge
    \setbox1=\hbox{\raise \@tempdima\hbox to 0pt{%
        \hskip #1\feyn@mfmodule \box0\hss}}%
    \ht1=0pt \dp1=0pt \box1}
\def\feyn@pos@ulft#1#2#3{% ulft
    \leavevmode
    \@tempdima=#2\feyn@mfmodule \advance\@tempdima\feyn@nudge
    \setbox1=\hbox{\raise \@tempdima\hbox to 0pt{%
        \hskip #1\feyn@mfmodule
        \hbox to 0pt{\hss$\scriptstyle #3$\hskip\feyn@nudge}\hss}}%
    \ht1=0pt \dp1=0pt \box1}
%    \end{macrocode}
%
% Now include the definitions of the annotation positions, as extracted
% from the Metafont file.  These define macros |\feyn@ann@#1|,
% where argument |#1| is a given character (or ligature) at the
% position |(#2,#3)|, using  the various |\feyn@pos@<x>| macros.  The
% |<x>| is either the value of argument |#4|, or the contents of
% |\@tempa| if that has been set non-empty by |\momentum@|.
%    \begin{macrocode}
\def\feyn@annotation#1#2#3#4{%
    \expandafter\def\csname feyn@ann@#1\endcsname##1{%
        \csname feyn@pos@\ifx\@tempa\@empty #4\else\@tempa\fi\endcsname
            {#2}{#3}{##1}%
    #1}}
%    \end{macrocode}
% Now read in the collection of annotation positions.  These are
% generated by the \texttt{./parse-ligtables} script, and inserted
% into this file by the Makefile when \file{feyn.dtx} is generated.
%    \begin{macrocode}
% @FEYNANNOTATIONS@
% commands generated by parse-ligtables...
\feyn@annotation{f}{0.99974}{0.35}{top}% 102 = "f"
\feyn@annotation{fA}{0.99974}{0.35}{top}% 70 = "F"
\feyn@annotation{fV}{0.99974}{0.35}{top}% 6 = 6
\feyn@annotation{flo}{0}{2.25}{top}% 107 = "k"
\feyn@annotation{floA}{0}{2.25}{top}% 75 = "K"
\feyn@annotation{floV}{0}{2.25}{top}% 11 = 11
\feyn@annotation{fu}{0.70692}{0.95692}{ulft}% 101 = "e"
\feyn@annotation{fuA}{0.70692}{0.95692}{ulft}% 69 = "E"
\feyn@annotation{fuV}{0.70692}{0.95692}{ulft}% 5 = 5
\feyn@annotation{fd}{0.70692}{0.95692}{urt}% 100 = "d"
\feyn@annotation{fdA}{0.70692}{0.95692}{urt}% 68 = "D"
\feyn@annotation{fdV}{0.70692}{0.95692}{urt}% 4 = 4
\feyn@annotation{fv}{0}{1.24974}{urt}% 98 = "b"
\feyn@annotation{fvA}{0}{1.24974}{urt}% 66 = "B"
\feyn@annotation{fvV}{0}{1.24974}{urt}% 2 = 2
\feyn@annotation{m}{0.99974}{0.32802}{top}% 109 = "m"
\feyn@annotation{mA}{0.99974}{0.32802}{top}% 77 = "M"
\feyn@annotation{mV}{0.99974}{0.32802}{top}% 13 = 13
\feyn@annotation{ms}{0.49986}{0.32802}{top}% 35 = "#"
\feyn@annotation{fl}{0}{1.75}{top}% 108 = "l"
\feyn@annotation{flA}{0}{1.75}{top}% 76 = "L"
\feyn@annotation{flV}{0}{1.75}{top}% 12 = 12
\feyn@annotation{flu}{0}{-1.25}{bot}% 110 = "n"
\feyn@annotation{fluA}{0}{-1.25}{bot}% 78 = "N"
\feyn@annotation{fluV}{0}{-1.25}{bot}% 14 = 14
\feyn@annotation{flS}{0}{1.16667}{top}% 111 = "o"
\feyn@annotation{flSA}{0}{1.16667}{top}% 79 = "O"
\feyn@annotation{flSV}{0}{1.16667}{top}% 15 = 15
\feyn@annotation{flSu}{0}{-0.83334}{bot}% 119 = "w"
\feyn@annotation{flSuA}{0}{-0.83334}{bot}% 87 = "W"
\feyn@annotation{flSuV}{0}{-0.83334}{bot}% 23 = 23
\feyn@annotation{g}{0.99974}{0.45}{top}% 103 = "g"
\feyn@annotation{gA}{0.99974}{0.45}{top}% 71 = "G"
\feyn@annotation{gV}{0.99974}{0.45}{top}% 7 = 7
\feyn@annotation{gu}{0.70692}{0.95692}{ulft}% 117 = "u"
\feyn@annotation{guA}{0.70692}{0.95692}{ulft}% 85 = "U"
\feyn@annotation{guV}{0.70692}{0.95692}{ulft}% 21 = 21
\feyn@annotation{gd}{0.70692}{0.95692}{urt}% 118 = "v"
\feyn@annotation{gdA}{0.70692}{0.95692}{urt}% 86 = "V"
\feyn@annotation{gdV}{0.70692}{0.95692}{urt}% 22 = 22
\feyn@annotation{gv}{0}{1.24974}{urt}% 125 = "}"
\feyn@annotation{gvA}{0}{1.24974}{urt}% 93 = "]"
\feyn@annotation{gvV}{0}{1.24974}{urt}% 29 = 29
\feyn@annotation{g1}{-1}{1.98206}{ulft}% 113 = "q"
\feyn@annotation{g1A}{-1}{1.98206}{ulft}% 81 = "Q"
\feyn@annotation{g1V}{-1}{1.98206}{ulft}% 17 = 17
\feyn@annotation{g2}{1.41422}{1.66422}{urt}% 114 = "r"
\feyn@annotation{g2A}{1.41422}{1.66422}{urt}% 82 = "R"
\feyn@annotation{g2V}{1.41422}{1.66422}{urt}% 18 = 18
\feyn@annotation{g3}{1.41422}{-1.16422}{lrt}% 115 = "s"
\feyn@annotation{g3A}{1.41422}{-1.16422}{lrt}% 83 = "S"
\feyn@annotation{g3V}{1.41422}{-1.16422}{lrt}% 19 = 19
\feyn@annotation{g4}{-1}{-1.48206}{llft}% 116 = "t"
\feyn@annotation{g4A}{-1}{-1.48206}{llft}% 84 = "T"
\feyn@annotation{g4V}{-1}{-1.48206}{llft}% 20 = 20
\feyn@annotation{gl}{0}{1.75}{urt}% 121 = "y"
\feyn@annotation{glA}{0}{1.75}{urt}% 89 = "Y"
\feyn@annotation{glV}{0}{1.75}{urt}% 25 = 25
\feyn@annotation{glu}{0}{-1.25}{llft}% 122 = "z"
\feyn@annotation{gluA}{0}{-1.25}{llft}% 90 = "Z"
\feyn@annotation{gluV}{0}{-1.25}{llft}% 26 = 26
\feyn@annotation{glB}{1.02051}{2.71367}{urt}% 123 = "{"
\feyn@annotation{glBA}{1.02051}{2.71367}{urt}% 91 = "["
\feyn@annotation{glBV}{1.02051}{2.71367}{urt}% 27 = 27
\feyn@annotation{glS}{0}{1.5833}{llft}% 124 = "|"
\feyn@annotation{glSA}{0}{1.5833}{llft}% 92 = "\"
\feyn@annotation{glSV}{0}{1.5833}{llft}% 28 = 28
\feyn@annotation{h}{0.99974}{0.25}{top}% 104 = "h"
\feyn@annotation{hA}{0.99974}{0.25}{top}% 72 = "H"
\feyn@annotation{hV}{0.99974}{0.25}{top}% 8 = 8
\feyn@annotation{hu}{0.70464}{0.95464}{ulft}% 105 = "i"
\feyn@annotation{huA}{0.70464}{0.95464}{ulft}% 73 = "I"
\feyn@annotation{huV}{0.70464}{0.95464}{ulft}% 9 = 9
\feyn@annotation{hd}{0.70464}{0.95464}{urt}% 106 = "j"
\feyn@annotation{hdA}{0.70464}{0.95464}{urt}% 74 = "J"
\feyn@annotation{hdV}{0.70464}{0.95464}{urt}% 10 = 10
\feyn@annotation{hl}{0}{1.75}{top}% 126 = "~"
\feyn@annotation{hlA}{0}{1.75}{top}% 94 = "^"
\feyn@annotation{hlV}{0}{1.75}{top}% 30 = 30
\feyn@annotation{hlu}{0}{-1.25}{top}% 127 = 127
\feyn@annotation{hluA}{0}{-1.25}{top}% 95 = "_"
\feyn@annotation{hluV}{0}{-1.25}{top}% 31 = 31
\feyn@annotation{hs}{0.49986}{0.25}{top}% 34 = """
\feyn@annotation{c}{0.65044}{0.90044}{top}% 99 = "c"
\feyn@annotation{p}{0.65}{0.9}{top}% 112 = "p"
\feyn@annotation{P}{0.65044}{0.90044}{top}% 80 = "P"
\feyn@annotation{x}{0}{0.55641}{top}% 120 = "x"
%    \end{macrocode}
%
%
% The |\momentum| macro (finally) invokes its worker macro
% |\momentum@|, defaulting that macro's optional argument to empty.
% In fact the macro |\momentum| should be only rarely
% invoked, since ! is made active and bound to it within |\feyn|.
%
% The |\momentum@| macro takes two arguments, and expands to a call to
% macro |\feyn@ann@#1|, acting on the second argument.  This macro is
% one of those defined by |\feyn@annotation| above.  There is an
% optional argument, giving the position for the annotation, if it has
% turned out that the default position for this character is
% inappropriate.  The adjusted position may be one of `top', `urt',
% `lrt', `bot', `llft' or `ulft'.
%    \begin{macrocode}
\def\momentum{\@ifnextchar[\momentum@{\momentum@[]}}
\def\momentum@[#1]#2#3{%
  \def\@tempa{#1}
  \ifx\@tempa\@empty \else
    \@ifundefined{feyn@pos@#1}
        {\@latex@error{No annotation position #1}%
           {You cannot call \string\momentum[#1]{...}^^J(must be one
             of top, urt, lrt, bot, llft, ulft)}%
        #2}%
  \fi
  \@ifundefined{feyn@ann@#2}%
    {\@latex@error{No annotation defined for #2}%
      {You cannot call \string\momentum{#2}{...}}%
     #2}%
  {\csname feyn@ann@#2\endcsname{#3}}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\vertexlabel}
% The command |\vertexlabel^{text}| or |\vertexlabel_{text}| positions
% the |{text}| in maths mode either above or below, respectively, the
% current position.  It's used between characters to label a vertex.
%    \begin{macrocode}
\def\vertexlabel#1#2{\setbox0=\hbox to 0pt{\hss$\scriptstyle #2$\hss}
  \ifcat #1^
    \vbox to 0pt{\vss\box0\nointerlineskip\kern2\feyn@maxis}
  \else\ifcat #1_
    \vbox to 0pt{\kern\feyn@maxis\nointerlineskip\box0\vss}
  \else
    \PackageError{feyn}
      {Bad arguments for \string\vertexlabel}
      {Usage: \string\vertexlabel^{text} or \string\vertexlabel_{text}}
  \fi\fi
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\annotate}
% The |\annotate| command takes $x$ and $y$ coordinates in units of
% modules, and text (in math mode) to be placed on a |\diagram|.
% Deprecated, now that the characters have annotation built in to them.
%    \begin{macrocode}
\def\annotate#1#2#3{\vcenter to 0pt{\vss
    \hbox to 0pt{\hskip #1\feyn@module\hbox to 0pt{\hss$\scriptstyle #3$\hss}\hss
    }\vskip #2\feyn@module}}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\tannotate}
% The |\tannotate| command is just the same, but the annotating text
% is in horizontal mode.
%    \begin{macrocode}
\def\tannotate#1#2#3{\vcenter to 0pt{\vss
    \hbox to 0pt{\hskip #1\feyn@module\hbox to 0pt{\hss #3\hss}\hss
    }\vskip #2\feyn@module}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\feynstrut}
% The macro |\feynstrut#1#2| defines |\strut| to have a height
% |#1| modules, and depth |#2| modules.
%    \begin{macrocode}
\def\feynstrut#1#2{\setbox\strutbox=\hbox{\vrule
	height #1\feyn@module depth #2\feyn@module width 0pt}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\arrow}
% The command |\arrow#1#2#3| puts an arrow of gradient |#3|${}\times 45^\circ$
% at position |(#1,#2)|(modules).  This doesn't work -- the |\char|
% results in a |\rm| character appearing, rather than a |\feyn|
% character.  Putting in a symbol like `+' has the same effect, but
% putting in, say, `a' works as expected.  In other words, it's to do
% with the character's mathcode, and the |\char|
% should be replaced by a |\mathchar"7?\@tempcnta| somehow.  The
% problem is that that depends on the parameter |\fam| having a
% suitable value.  It's not clear to me what this corresponds to in
% \LaTeXe.  See the \TeX book, chapter 17.
%    \begin{macrocode}
\def\arrow#1#2#3{\@latex@error{Do not use the \string\arrow macro any more}{}}
%    \end{macrocode}
% \end{macro}
%
% Declare symbols.  All of these are ligatures.
%    \begin{macrocode}
\DeclareMathSymbol{\wfermion}{0}{feynman}{"64}
%\DeclareMathSymbol{\Wfermion}{0}{feynman}{"44}
\DeclareMathSymbol{\hfermion}{0}{feynman}{"6B}
%\DeclareMathSymbol{\Hfermion}{0}{feynman}{"4B}
\DeclareMathSymbol{\shfermion}{0}{feynman}{"6C}
%\DeclareMathSymbol{\sHfermion}{0}{feynman}{"4C}
\DeclareMathSymbol{\whfermion}{0}{feynman}{"6D}
%\DeclareMathSymbol{\wHfermion}{0}{feynman}{"4D}
\DeclareMathSymbol{\gvcropped}{0}{feynman}{"07}
%    \end{macrocode}
% But the following are not ligatures.
%    \begin{macrocode}
\DeclareMathSymbol{\bigbosonloop}{0}{feynman}{"7B}
%\DeclareMathSymbol{\Bigbosonloop}{7}{feynman}{"21}
\DeclareMathSymbol{\smallbosonloop}{0}{feynman}{"7C}
\DeclareMathSymbol{\bigbosonloopA}{0}{feynman}{"5B}
\DeclareMathSymbol{\smallbosonloopA}{0}{feynman}{"5C}
\DeclareMathSymbol{\bigbosonloopV}{0}{feynman}{"1B}
\DeclareMathSymbol{\smallbosonloopV}{0}{feynman}{"1C}
%    \end{macrocode}
%
%
% \Finale
\endinput