% \iffalse % feynmf.dtx - Feynman diagrams with METAFONT for LaTeX(2e)
% Copyright (C) 1989, 1990, 1992-1994 by Thorsten.Ohl@Physik.TH-Darmstadt.de
% /home/sources/ohl/tex/feynmf/feynmf.dtx,v 1.5 1994/05/28 12:10:04 ohl Exp
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Feynmf is free software; you can redistribute it and/or modify it
% under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2, or (at your option)
% any later version.
%
% Feynmf is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
%
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%
% \fi
%
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%% 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
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% \MakeShortVerb{\|}
%
% \title{%
% \FMF: \\
% Drawing Feynman Diagrams \\
% with \LaTeX{} and \MF}
%
% \author{%
% Thorsten Ohl\thanks{e-mail:
% {\tt Thorsten.Ohl@Physik.TH-Darmstadt.de}}\\
% \hfil \\
% Technische Hochschule Darmstadt \\
% Schlo\ss gartenstr. 9 \\
% D-64289 Darmstadt \\
% Germany}
%
% \maketitle
% \begin{abstract}
% \FMF{} is a \LaTeX{} package for easy drawing of professional
% quality Feynman diagrams with \MF. \FMF{} lays out most
% diagrams satisfactorily from the structure of the graph without
% any need for manual intervention. Nevertheless all the power of
% \MF{} is available for the most obscure cases.
% \end{abstract}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \tableofcontents
% \begin{fmffile}{fmfsampl}
% \def\bottomfraction{0}
% \unitlength=1mm
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Introduction}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Purpose and scope}
%
% In recent years, \TeX\footnote{\TeX{} is a trademark of the American
% Mathematical Society.}~\cite{TeX}
% and \LaTeX\footnote{\LaTeX{} might be a trademark of Addison Wesley
% Publishing Company.}~\cite{LaTeX}
% have revolutionized the way
% we share information in theoretical physics (and other areas). Not
% only does \TeX{} provide typographical capabilities, which transcend
% those of commercial ``wordprocessors'' substantially, \TeX{} documents
% are also completely portable. Since implementations are available
% on essentially all computers in use in the community, documents can
% be shared without the usual restrictions of proprietary data
% formats. This has enabled us to collaborate on papers with
% colleagues on the other side of the globe, to replace the mailing of
% hard copy preprints by electronic transmission and to submit these
% papers electronically to the publisher.
%
% This portability comes with a price, though. \TeX{} (and \LaTeX)
% do not address the issue of graphical information, apart from the
% rudimentary (but very useful) capabilities of the \LaTeX{} |picture|
% environment and similar
% packages~\cite{LaTeX-Companion}, which provide line drawings like
% the one in figure~\ref{fig:flow}. As an de facto standard for the
% inclusion of more complex graphics has emerged the inclusion of
% PostScript~\footnote{PostScript is a trademark of Adobe Systems
% Inc.}
% files. The complete document can then
% be printed on any PostScript device.
%
% Still there are areas, where complementary approaches seem worth
% pursuing. In particular this is the case, if the graphical
% information is highly formalized, like the case at hand. Feynman
% diagrams are specified by their topology and the type of particles
% connecting the vertices. Thus a given diagram can be reproduced
% from a very concise specification, if the software is able to choose
% a reasonable layout (semi-)automatically.
%
% \MF\footnote{\MF{} is a trademark of Addison Wesley Publishing
% Company.}~\cite{MF}
% appears to be the perfect tool for such a purpose\footnote{%
% Another perfect tool is \MP~\protect\cite{MetaPost}, which is
% unfortunately not available without signing a non disclosure
% agreement with AT\&T. It is however hoped that \MP{} will be
% freed in the near future. \FMF{} supports \MF{} as
% well as \MP{} (under the names \texttt{feynmp.sty} and
% \texttt{feynmp.mp}).},
% since
% \begin{enumerate}
% \item{} it is part of any (reasonable) \TeX{} installation, thus
% available to all potential users,
% \item{} it has very powerful graphics primitivs, which allow high
% quality output, and
% \item{} it has builtin linear algebra, which allows us to choose a
% layout automatically.
% \end{enumerate}
% Still, providing at least the basic interface in \LaTeX{} macros
% seems appropriate for boosting the acceptance among the less
% technically oriented parts of the audience.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Relation to similar packages}
%
% Before we start, a couple of words about some complementary packages
% on the market are in order. First of all: I failed to do my
% homework and didn't try hard enough to find~\cite{hoenig} in a
% library. I'm sure that in there is a smarter way of returning
% information from \MF{} to \TeX{}. Those who don't know the
% literature are doomed to reinvent the wheel. But this isn't a
% scholarly work and reinventing the wheel was \emph{fun!}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Feynman}
%
% Micheal Levine's |feynman| package~\cite{levine} is
% implemented on top of the standard \LaTeX{} |picture|
% environment~\cite{LaTeX}. This makes it completely portable (no
% need for a correct \MF{} installation), but it requires manual
% layout and the graphics output is (though very useful) less than
% perfect.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Axodraw}
%
% Jos Vermaseren's |axodraw| package~\cite{axodraw} uses
% |\special|s to access PostScript primitives for drawing diagrams.
% This approach is inherently not portable (though the ubiquity of
% PostScript printers makes this a minor point) but at least as
% flexible as the present one. It still requires manual layout,
% though.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Historical note}
%
% This code has a rather long history\footnote{Which is a partial
% explanation, if not excuse, for its slightly incoherent structure.}.
% Most of the sections~\ref{sec:mf-basics}, \ref{sec:pictures},
% \ref{sec:shading}, and~\ref{sec:drawing} started in 1989 as
% |feynman.mf|, a library of \MF{} macros for drawing Feynman
% diagrams in my thesis. The layout had to be chossen completely
% manually, which required a long edit-process-preview cycle and made
% |feynman.mf| awkward to use.
% Nevertheless, it survived for five years without major
% modifications, only slight enhancements had been made. Early in
% 1994, I became aware of Thomas Leathrum's |mfpic|~\cite{mfpic}.
% This inspired me to shift the user interface from \MF{} to
% \LaTeX, because this allows a smoother blending of the \LaTeX{}
% |picture| environment with \FMF{}. While doing this and after
% having been taught by Tim Stelzer's and Bill Long's
% \texttt{MADGRAPH}~\cite{madgraph} that minimizing the length of the
% graph gives surprisingly good results for tree graphs\footnote{I had
% thought about this earlier myself, but foolishly discarded the idea.
% I didn't expect such a ``too simple'' method to give esthetically
% pleasing results for loop graphs, which were my main concern.}, I
% added the graph manipulation code in section~\ref{sec:graphs}.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Projects}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Virtual Graphs}
% \label{sec:virtual-pictures}
%
% In a future version, \FMF{} will be able to draw ``virtual''
% graphs, i.e.~graphs which are larger than the current limit enforced
% by numeric overflow at higher resolutions. This can be implemented
% by calculating the layout of a miniature graph and afterwards
% distributing the full graph among several \MF{} characters.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Conclusion}
%
% It goes without saying that \FMF{} is not perfect. There are
% cases where using a graphical drawing tool with a mouse will give
% more pleasing results in less time. But in most cases, \FMF{}
% will give satisfactory results without any fine tuning. These will
% be reproducible and independent from the computer it is running on.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Usage}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Invocation}
%
% Instructing \LaTeX{} to use \FMF{} is as simple as\footnote{As
% given, this applies to \LaTeXe. Adapting \FMF{} to \LaTeX{} v2.09
% should be simple.}
% \begin{verbatim}
% \usepackage{feynmf}
% \end{verbatim}
% and calling \MF{} should not be harder as
% \begin{verbatim}
% mf '\mode:=localmode; input foobar'
% \end{verbatim}
% where |foobar| is the name of your \MF{} output file.
% The hard part usually lies in instructing \TeX{} and your favorite
% |dvi|-driver how to find the generated |tfm| and |gf| (resp.~|pk|)
% files. This is highly system dependent and can be trivial (as in
% the standard UNIX\footnote{UNIX was a trademark of UNIX Systems
% Laboratory, but is rumored to have been donored to X/Open.}
% \TeX{} installations) or almost impossible (as
% under MVS). Please consult your local guide or local ``\TeX{}
% Wizards'' on this point.
%
% If you have \MP, then you can use it by placing
% \begin{verbatim}
% \usepackage[dvips]{feynmp}
% \end{verbatim}
% in your \LaTeX{} source. Here |dvips| is an option for the
% \LaTeXe{} |egraphics| package which is used for including the
% generated PostScript files. It should be replaced by your local
% supported |dvi| driver. Calling \MP{} is usually even simpler
% \begin{verbatim}
% mp foobar
% \end{verbatim}
% since there is no mode to be picked.
%
% Currently, \FMF{} will work only with \LaTeXe{}. Porting to
% \LaTeX2.09 should be a trivial exercise of replacing some
% convenience macros which are new with \LaTeXe\footnote{But who is
% still using \LaTeX2.09, anyway?} Porting to plain \TeX{} macro
% packages will require more work, because the |picture| environment
% is used. Anyway, it should be simple if the label mechanism is
% implemented on top
% {P\kern-.12em\lower.5ex\hbox{I}\kern-.075emC\kern-.11em\TeX}, |epic|
% or similar packages.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{figure}
% \begin{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \setlength{\unitlength}{0.012500in}%
% \begingroup\makeatletter\ifx\SetFigFont\undefined
% \def\x#1#2#3#4#5#6#7\relax{\def\x{#1#2#3#4#5#6}}%
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% \ifnum #1<34\Large\else \ifnum #1<41\LARGE\else
% \huge\fi\fi\fi\fi\fi\fi
% \csname #3\endcsname}%
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% \put(120,460){\vector( 1, 0){105}}
% \put(300,560){\vector( 0,-1){ 60}}
% \put(350,640){\vector( 0,-1){145}}
% \thicklines
% \put(105,494){\vector(-1,-1){0}}
% \multiput(211,600)(-3.19697,-3.19697){33}{\makebox(0.4444,0.6667){\SetFigFont{10}{12}{rm}.}}
% \put(160,790){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}\LaTeX{} \#1}}}
% \put(360,535){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}dvi2xxx}}}
% \put(350,725){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}\MF}}}
% \put( 3,663){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}\LaTeX{} \#2}}}
% \end{picture}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \end{center}
% \caption{Flow of information in a \FMF{} application: The
% first \LaTeX{} pass is shown with a dashed line. The \MF{}
% pass is shown with the full lines and the second \LaTeX{} pass
% with dotted lines. The final dvi translation step is shown with
% thin lines.}
% \label{fig:flow}
% \end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% The flow of information depicted in figure~\ref{fig:flow} looks much
% more complicated than it is. The important feature is that there a
% two sets of files which can be used to distribute a document:
% \begin{enumerate}
% \item{} Iff the recipient has a working \MF{} installation
% (which shouldn't be a problem, except for some impoverished
% commercial implementations), the document can be typset from the
% \LaTeX{} source \emph{alone}, by running \LaTeX{}, \MF{}
% and \LaTeX{} again (the latter step might have to be repeated to
% get cross references right).
% \item{} Another possibility (which doesn't require \MF{} on
% the recipient's side), is to distribute the \LaTeX{} source, the
% |tfm| and |gf| files (or |pk| files respectively) along with the
% label files with extension |t|$n$ (where $n$ as an integer).
% Distributing the \MF{} |log| files is a possible alternative
% for the latter, but discouraged, because these are prone to be
% erased accidentally.
% \end{enumerate}
%
% I should add one caveat here: some |dvi| file previewers
% (e.g.~xdvi(1) under UNIX) do \emph{not} reread font information if
% the |tfm| or |pk| files have changed, even though they reread the
% |dvi| file if it has changed. Thus you have to restart such
% previewers if you have made changes in diagrams to see these changes
% on the screen.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{figure}
% \begin{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \setlength{\unitlength}{0.012500in}%
% \begingroup\makeatletter\ifx\SetFigFont\undefined
% \def\x#1#2#3#4#5#6#7\relax{\def\x{#1#2#3#4#5#6}}%
% \expandafter\x\fmtname xxxxxx\relax \def\y{splain}%
% \ifx\x\y % LaTeX or SliTeX?
% \gdef\SetFigFont#1#2#3{%
% \ifnum #1<17\tiny\else \ifnum #1<20\small\else
% \ifnum #1<24\normalsize\else \ifnum #1<29\large\else
% \ifnum #1<34\Large\else \ifnum #1<41\LARGE\else
% \huge\fi\fi\fi\fi\fi\fi
% \csname #3\endcsname}%
% \else
% \gdef\SetFigFont#1#2#3{\begingroup
% \count@#1\relax \ifnum 25<\count@\count@25\fi
% \def\x{\endgroup\@setsize\SetFigFont{#2pt}}%
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% \csname \romannumeral\the\count@ pt\expandafter\endcsname
% \csname @\romannumeral\the\count@ pt\endcsname
% \csname #3\endcsname}%
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% \begin{picture}(357,400)(3,420)
% \thinlines
% \put( 40,740){\framebox(80,80){}}
% \put( 55,795){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{tt}foo.tex}}}
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% \thicklines
% \put(295,760){\vector(-1,-1){ 82}}
% \put(295,760){\vector(-2,-1){164}}
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% \put(160,790){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}\LaTeX \#1}}}
% \put( 3,663){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}\LaTeX \#2}}}
% \put(345,520){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}dvips}}}
% \put(340,685){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}\MP}}}
% \end{picture}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \end{center}
% \caption{Flow of information in a \FMF{} application if \MP{} is
% used instead of \MF.}
% \label{fig:flowp}
% \end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Basic usage}
%
% The basic features of \FMF{} are (or rather ``should be'')
% available through the \LaTeX{} interface. Not knowledge of
% \MF{} is necessary.
%
% \DescribeEnv{fmffile}
% Upto 255 characters can be placed into one \MF{} file, they are
% enclosed in a single |fmffile| environment. The environment
% takes the filename as argument. Currently \FMF{} does \emph{not}
% check that the 255 character limit per file is not overrun.
% \begin{verbatim}
% \begin{fmffile}{foobar}
% ...
% \end{fmffile}
% \end{verbatim}
%
% \DescribeEnv{fmfchar}
% Draw one character and place it here. Arguments are
% |(|\meta{width}|,|\meta{height}|)| as in:
% \begin{verbatim}
% \begin{fmfchar}(40,25)
% ...
% \end{fmfchar}
% \end{verbatim}
%
% \DescribeEnv{fmfchar*}
% Same as |fmfchar|, but enclosed in a |picture| environment of the
% same size and supporting \LaTeX{} labels.
% \begin{verbatim}
% \begin{fmfchar*}(40,25)
% ...
% \end{fmfchar*}
% \end{verbatim}
%
% \DescribeMacro{\fmfincoming}
% \DescribeMacro{\fmfoutgoing}
% \DescribeMacro{\fmfsurround}
% Positioning of
% external vertices has to done explicitely. The technical reason is
% that they would otherwise collapse with their neighbors, but
% practical reasons also suggest to give the user full control here.
% |\fmfincoming{|\meta{v1}$[$|,|\ldots$]$|}| places the
% vertices in the comma separated list \meta{v1},\ldots
% equidistantly on a smooth path on the left side of the diagram.
% |\fmfoutgoing{|\meta{v1}$[$|,|\ldots$]$|}| does the same
% thing on the right.
% |\fmfsurround{|\meta{v1}$[$|,|\ldots$]$|}|
% places its arguments on smooth path
% surrounding the diagram:
% \begin{center}
% \label{p:galleries}
% \fbox{\begin{fmfchar}(25,20)
% \fmfpen{thick}%
% \fmfincoming{i1,i2,i3,i4}%
% \fmfdot{i1,i2,i3,i4}%
% \fmfcmd{draw (in_gallery);}
% \end{fmfchar}}\qquad
% \fbox{\begin{fmfchar}(25,20)
% \fmfpen{thick}%
% \fmfoutgoing{o1,o2,o3,o4}%
% \fmfdot{o1,o2,o3,o4}%
% \fmfcmd{draw (out_gallery);}
% \end{fmfchar}}\qquad
% \fbox{\begin{fmfchar}(25,20)
% \fmfpen{thick}%
% \fmfsurround{e1,e2,e3,e4,e5,e6,e7}%
% \fmfdot{e1,e2,e3,e4,e5,e6,e7}%
% \fmfcmd{draw (surround_gallery);}
% \end{fmfchar}}
% \end{center}
% The former two are more useful in the
% context of diagrams for scattering matrix elements, while the latter
% can be used for general Green's functions.
%
% \DescribeMacro{\fmfpen}
% Pick up a pen of the specified size. |\fmfpen{|\meta{weight}|}|
% is used for changing the weight (i.e.~thickness) of the lines.
% Predefined sizes are |thin| and |thick|.
%
% \def\linesample#1{%
% \begin{fmfchar}(30,4)
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2}
% \fmf{#1}{i1,o1}
% \end{fmfchar}}
% \begin{table}
% \begin{tabular}{rcp{60mm}}
% Name & Example & Notes \\\hline
% |boson| & \linesample{boson} &
% |wiggly_len| gives distance of wiggles \\
% |dashes| & \linesample{dashes} &
% |dash_len| gives length of dashes \\
% |dots| & \linesample{dots} &
% |dot_len| gives distance of dashes \\
% |double| & \linesample{double} & \\
% |electron| & \linesample{electron} & \\
% |fermion| & \linesample{fermion} & \\
% |ghost| & \linesample{ghost} & \\
% |gluon| & \linesample{gluon} &
% |curly_len| gives distance of curls.\hfil\goodbreak
% See also figure~\ref{fig:gluons} \\
% |heavy| & \linesample{heavy} & heavy quarks (HQET) \\
% |phantom| & \linesample{phantom} &
% (yes, this \emph{is} empty!) \\
% |photon| & \linesample{photon} &
% |wiggly_len| gives distance of wiggles \\
% |plain| & \linesample{plain} & \\
% |quark| & \linesample{quark} & \\
% |scalar| & \linesample{scalar} &
% |dash_len| gives length of dashes \\
% |vanilla| & \linesample{vanilla} &
% \end{tabular}
% \caption{Available line styles}
% \label{tab:line-styles}
% \end{table}
%
% \begin{table}
% \begin{tabular}{rp{60mm}}
% Name & Explanation \\\hline
% |tension| & draw a tighter ($>1$) or looser ($<1$) arc \\
% |left| & draw on a halfcircle on the left \\
% |right| & draw on a halfcircle on the right \\
% |straight| & draw on a straight line \\
% |label| & \TeX{} text for labeling the arc \\
% |side| & force placement of the label on the |left| or
% |right| \\
% |dist| & place label at a distance |dist|
% \end{tabular}
% \caption{Available line options}
% \label{tab:line-options}
% \end{table}
%
% \DescribeMacro{\fmf}
% This is the the most frequently used macro in \FMF{} applications.
% |\fmf{|\meta{style}\allowbreak
% $[$|,|\meta{opt}\allowbreak
% $[$|=|\meta{val}$]$|,|\ldots$]$|}{|\meta{v1}|,|\meta{v2}\allowbreak
% $[$|,|\ldots$]$|}|
% connects the vertices \textit{v1,v2,\ldots} with a line of style
% \meta{style}, using a set of options \meta{opt} with (optional)
% value \meta{val}. If a vertex is not
% known yet, it is added to the diagram. Note that the actual drawing
% is not done immediately, because the positions can only be
% calculated when \emph{all} vertices are known. The currently
% available styles are collected in table~\ref{tab:line-styles}. Most
% names should be self explanatory\footnote{At least for the likely
% users of \FMF!} and are not discussed further. The |phantom|
% style is special, because it
% only enters the vertices and does \emph{not} cause a line to be
% drawn. This is extremely useful for advanced layout features, as
% explained below.
% The supported options are collected in
% table~\ref{tab:line-options}\footnote{%
% \begin{dubious}
% One particulary useful further option would be \texttt{smooth},
% allowing for several lines joined smoothly. Early
% experimentation has shown however, that the results are not
% always what one expects and that there is a lot of room for
% abuse.
% \end{dubious}}.
%
% \begin{table}
% \begin{tabular}{rp{60mm}}
% Name & Explanation \\\hline
% |blob| & draw a shaded blob of the given diameter at the
% vertex \\
% |dot| & draw a dot at the vertex
% \end{tabular}
% \caption{Available vertex shapes}
% \label{tab:vertex-shapes}
% \end{table}
%
% \begin{table}
% \begin{tabular}{rp{60mm}}
% Name & Explanation \\\hline
% |label| & \TeX{} text for labeling the vertex \\
% |angle| & force placement of the label at the given angle from
% the vertex \\
% |dist| & place label at a distance |dist|
% \end{tabular}
% \caption{Available vertex options}
% \label{tab:vertex-options}
% \end{table}
%
% \DescribeMacro{\fmfv}
% Declare vertices with options:
% |\fmfv{|\meta{shape}$[$|=|\meta{val}$]$\allowbreak
% $[$|,|\meta{opt}\allowbreak
% $[$|=|\meta{val}$]$|,|\ldots$]$|}{|\meta{v1}\allowbreak
% $[$|,|\ldots$]$|}|
% Currently it is only used for adding labels to a vertex. Supported
% shapes are listed in table~\ref{tab:vertex-shapes}, and supported
% options are collected in table~\ref{tab:vertex-options}\footnote{%
% \begin{dubious}
% This will be generalized to give more shapes.
% Apart from predefined shapes, we will have userdefined paths
% specifying arbitrary shapes.
% \end{dubious}}.
%
% \DescribeMacro{\fmfblob}
% Draw a blob of the specified diameter at the vertices.
% |\fmfblob{|\meta{diameter}|}{|\meta{v1}\allowbreak
% $[$|,|\ldots$]$|}| is equivalent to
% |\fmfv{blob=|\meta{diameter}\allowbreak
% $[$|,|\meta{opt}\allowbreak
% $[$|=|\meta{val}$]$|,|\ldots$]$|}{|\meta{v1}\allowbreak
% $[$|,|\ldots$]$|}|
%
% \DescribeMacro{\fmfdot}
% Draw a dot at the vertices given as arguments.
% |\fmfdot{|\meta{v1}\allowbreak
% $[$|,|\ldots$]$|}| is equivalent to
% |\fmfv{dot|$[$|,|\meta{opt}\allowbreak
% $[$|=|\meta{val}$]$|,|\ldots$]$|}{|\meta{v1}\allowbreak
% $[$|,|\ldots$]$|}|
%
% \DescribeMacro{\fmfposition}
% Calculate the positions of the vertices based on the arcs which are
% defined up to this point. Usually this calculation is performed
% automatically at the end of the |fmfchar| environment. Calling it
% explicitely, is useful for adding arcs which should not enter the
% calculation.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Examples}
%
% As an example, consider drawing a straightforward box diagram,
% familier from $K$-$\bar K$, $D$-$\bar D$, and $B$-$\bar B$ mixing.
% The commands for the labels are not shown here, they are discussed
% in section~\ref{sec:labels}
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% We start the diagram and pick up a thick pen:
% \begin{verbatim}
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \end{verbatim}
% The incoming and outcoming vertices are placed on the left and
% right hand side, respectively:
% \begin{verbatim}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2}
% \end{verbatim}
% Now we tell \FMF{} how the arcs are connected.
% \begin{verbatim}
% \fmf{fermion}{i1,v1,v3,o1}
% \fmf{fermion}{o2,v4,v2,i2}
% \fmf{photon}{v1,v2}
% \fmf{photon}{v3,v4}
% \end{verbatim}
% Finally we tell \FMF{} to draw dots at the vertices and we're
% done.
% \begin{verbatim}
% \fmfdot{v1,v2,v3,v4}
% \end{fmfchar}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.35\linewidth}
% \begin{center}
% \begin{fmfchar*}(40,25)
% \fmfpen{thick}
% \fmfincoming{i1,i2}
% \fmflabel{$\noexpand\bar b$}{i1}
% \fmflabel{$d$}{i2}
% \fmfoutgoing{o1,o2}
% \fmflabel{$\noexpand\bar d$}{o1}
% \fmflabel{$b$}{o2}
% \fmf{fermion}{i1,v1}
% \fmf{fermion,label=$\noexpand\bar t,,\noexpand\bar c,,
% \noexpand\bar u$,side=right}{v1,v3}
% \fmf{fermion}{v3,o1}
% \fmf{fermion}{o2,v4}
% \fmf{fermion,label=$t,,c,,u$,side=right}{v4,v2}
% \fmf{fermion}{v2,i2}
% \fmf{photon,label=$W^+$,side=left}{v1,v2}
% \fmf{photon,label=$W^-$,side=right}{v3,v4}
% \fmfdot{v1,v2,v3,v4}
% \end{fmfchar*}
% \end{center}
% \end{minipage}
% \label{page:simple-examples}
%
% Here is the resonant $s$-channel contribution to $e^+e^-\to 4f$.
% (From now on, we do no longer display the
% |\begin{fmfchar}(40,25)|, |\fmfpen{thick}|, \ldots,
% |\end{fmfchar}| surrounding all pictures.)
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmf{fermion}{i1,v1,i2}
% \fmf{photon}{v1,v2}
% \fmfblob{.15w}{v2}
% \fmf{photon}{v2,v3}
% \fmf{fermion}{o1,v3,o2}
% \fmf{photon}{v2,v4}
% \fmf{fermion}{o4,v4,o3}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.38\linewidth}
% \begin{center}
% \fmfframe(0,5)(5,7){%
% \begin{fmfchar*}(40,25)
% \fmfpen{thick}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmflabel{$e_-$}{i1}
% \fmflabel{$e_+$}{i2}
% \fmf{fermion}{i1,v1,i2}
% \fmf{photon}{v1,v2}
% \fmfblob{.15w}{v2}
% \fmf{photon}{v2,v3}
% \fmflabel{$\noexpand\mu_+$}{o1}
% \fmflabel{$\noexpand\nu_{\noexpand\mu}$}{o2}
% \fmf{fermion}{o1,v3,o2}
% \fmf{photon}{v2,v4}
% \fmflabel{$\noexpand\bar c$}{o4}
% \fmflabel{$s$}{o3}
% \fmf{fermion}{o4,v4,o3}
% \end{fmfchar*}}
% \end{center}
% \end{minipage}
%
% And the resonant $t$-channel contribution:
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmf{fermion}{i1,v1,v2,i2}
% \fmf{photon}{v1,v3}
% \fmf{fermion}{o1,v3,o2}
% \fmf{photon}{v2,v4}
% \fmf{fermion}{o4,v4,o3}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.38\linewidth}
% \begin{center}
% \fmfframe(0,5)(5,7){%
% \begin{fmfchar*}(40,25)
% \fmfpen{thick}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmflabel{$e_-$}{i1}
% \fmflabel{$e_+$}{i2}
% \fmf{fermion}{i1,v1,v2,i2}
% \fmf{photon}{v1,v3}
% \fmflabel{$\noexpand\mu_+$}{o1}
% \fmflabel{$\noexpand\nu_{\noexpand\mu}$}{o2}
% \fmf{fermion}{o1,v3,o2}
% \fmf{photon}{v2,v4}
% \fmflabel{$\noexpand\bar c$}{o4}
% \fmflabel{$s$}{o3}
% \fmf{fermion}{o4,v4,o3}
% \end{fmfchar*}}
% \end{center}
% \end{minipage}
%
% Actually, these three diagrams can be improved slightly by using
% |phantom| arcs, which will be discussed in the next section.
%
% Two point loop diagrams pose another set of problems. We
% must have a way of specifying that one or more of the lines
% connecting the two vertices are \emph{not} connected by a straight
% line. The options |left|, |right| and |straight| offer the
% possibility to connect two vertices by a semicircle detour, either
% on the left or on the right. Since by default all lines contribute
% to the tension between two vertices, the |tension| option allows us
% to reduce this tension. The next examples shows both options in
% action. The lower fermion line is given an tension of~$1/3$ to
% make is symmetrical with the upper line with consists of three parts.
% The loop photon is using a detour on the right and does not
% contribute any tension.
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1}
% \fmf{fermion,tension=1/3}{i1,v1}
% \fmf{plain}{v1,v2}
% \fmf{fermion}{v2,v3}
% \fmf{photon,right,tension=0}{v2,v3}
% \fmf{plain}{v3,i2}
% \fmf{photon}{v1,o1}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.35\linewidth}
% \begin{center}
% \begin{fmfchar*}(40,25)
% \fmfpen{thick}
% \fmfincoming{i1,i2}
% \fmflabel{$p^{\noexpand\prime}$}{i1}
% \fmflabel{$p$}{i2}
% \fmfoutgoing{o1}
% \fmflabel{$p+p^{\noexpand\prime}$}{o1}
% \fmf{fermion,tension=1/3}{i1,v1}
% \fmf{plain}{v1,v2}
% \fmf{fermion,label=$p-k$,side=left}{v2,v3}
% \fmf{photon,right,tension=0,label=$k$}{v2,v3}
% \fmf{plain}{v3,i2}
% \fmf{photon}{v1,o1}
% \end{fmfchar*}
% \end{center}
% \end{minipage}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Labels}
% \label{sec:labels}
%
% Let us now come back to the examples on
% page~\pageref{page:simple-examples} and discuss how to add the
% labels.
%
% \DescribeMacro{\fmflabel}
% The macro |\fmflabel{|\meta{label}|}{|\meta{v}|}| adds the label
% \meta{label} to the vertex \meta{v}. In the current implementation,
% there can be only a single label for each vertex. Thus earlier
% calls to |\fmflabel| for the same vertex will be overwritten.
% \meta{label} will be placed with the |\put| command of the \LaTeX{}
% |picture| environment. \emph{It is absolutely necessary to quote
% \emph{each} \TeX{} control sequence appearing in \meta{label} with}
% |\noexpand|. \emph{Otherwise all kinds of disasters are bound to
% happen, causing at the very least some obscure error messages!}
%
% |\fmflabel| gives the user \emph{no} control on the placement of
% the the label (see below for a more fine-grained control provided by
% the options to the |\fmfv| macro). The label is placed using the
% following algorithm:
% \begin{enumerate}
% \item{} The reference point of the box containing \meta{label} is
% placed at the distance |3thick| on the continuation of the
% straight line connecting the center of the picture with the
% vertex \meta{v}.
% \item{} The reference point of the box is chosen such that the
% contents of the box is on the outside of the vertex (with
% respect to the center of the diagram). It is chosen from the
% four corners and the four midpoints of the sides.
% \end{enumerate}
%
% Therefore the four external particles in the~$B$-$\bar B$ mixing
% diagram on page~\pageref{page:simple-examples} are labelled simply
% by:
% \begin{verbatim}
% \fmflabel{$\noexpand\bar b$}{i1}
% \fmflabel{$d$}{i2}
% \fmflabel{$\noexpand\bar d$}{o1}
% \fmflabel{$b$}{o2}
% \end{verbatim}
%
% \begin{dubious}
% Explain more of the |label| option and the default placement rules.
% \end{dubious}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Advanced usage}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Tight arcs}
%
% If you add to any arc one or more |phantom| arcs they will cause
% a tighter bonding between the vertices involved
% \begin{verbatim}
% \fmf{fermion}{v1,v2}
% \fmf{phantom}{v1,v2}
% \end{verbatim}
% which is equivalent to
% \begin{verbatim}
% \fmf{fermion,tension=2}{v1,v2}
% \end{verbatim}
% The |phantom| arc has to be added \emph{before} any |\fmfposition|
% involving these vertices, of course. Here is an example from deep
% inelastic scattering. (We do not show the |\fmfcmd{}|s in this
% example which are used for decorating the incoming proton and do not
% affect \FMF's layout decisions.)
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{ip,il}
% \fmfoutgoing{oq1,oq2,d1,oq3,d2,d3,ol}
% \fmf{fermion}{ip,vp,vq,oq3}
% \fmf{fermion}{vp,oq1}
% \fmf{fermion}{vp,oq2}
% \fmf{photon}{vl,vq}
% \fmf{fermion}{il,vl,ol}
% \fmfblob{.15w}{vp}
% \fmfdot{vq}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.35\linewidth}
% \begin{center}
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \fmfincoming{ip,il}
% \fmfoutgoing{oq1,oq2,d1,oq3,d2,d3,ol}
% \fmf{fermion}{ip,vp,vq,oq3}
% \fmf{fermion}{vp,oq1}
% \fmf{fermion}{vp,oq2}
% \fmf{photon}{vl,vq}
% \fmf{fermion}{il,vl,ol}
% \fmfposition
% \fmfforce{vloc ip+(0,2thick)}{ipp}
% \fmfforce{vloc ip-(0,2thick)}{ipm}
% \fmfforce{vloc vp+(0,2thick)}{vpp}
% \fmfforce{vloc vp-(0,2thick)}{vpm}
% \fmfshift{0.12 (vloc ip - vloc vp)}{vpp}
% \fmfshift{0.10 (vloc ip - vloc vp)}{vpm}
% \fmf{plain}{ipp,vpp}
% \fmf{plain}{ipm,vpm}
% \fmfblob{.15w}{vp}
% \fmfdot{vq}
% \end{fmfchar}
% \end{center}
% \end{minipage}
%
% As it stands, all vertices come out too far to the right, because
% the greater number of outgoing lines pulls them over. Adding
% |\fmf{phantom}| makes the bond between the incoming vertices and the
% interactions tighter and produces a better balanced picture:
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{ip,il}
% \fmfoutgoing{oq1,oq2,d1,oq3,d2,d3,ol}
% \fmf{fermion}{ip,vp,vq,oq3}
% \fmf{phantom}{ip,vp}
% \fmf{fermion}{vp,oq1}
% \fmf{fermion}{vp,oq2}
% \fmf{photon}{vl,vq}
% \fmf{fermion}{il,vl,ol}
% \fmf{phantom}{il,vl}
% \fmfblob{.15w}{vp}
% \fmfdot{vq}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.35\linewidth}
% \begin{center}
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \fmfincoming{ip,il}
% \fmfoutgoing{oq1,oq2,d1,oq3,d2,d3,ol}
% \fmf{fermion}{ip,vp,vq,oq3}
% \fmf{phantom}{ip,vp}
% \fmf{fermion}{vp,oq1}
% \fmf{fermion}{vp,oq2}
% \fmf{photon}{vl,vq}
% \fmf{fermion}{il,vl,ol}
% \fmf{phantom}{il,vl}
% \fmfposition
% \fmfforce{vloc ip+(0,2thick)}{ipp}
% \fmfforce{vloc ip-(0,2thick)}{ipm}
% \fmfforce{vloc vp+(0,2thick)}{vpp}
% \fmfforce{vloc vp-(0,2thick)}{vpm}
% \fmfshift{0.16 (vloc ip - vloc vp)}{vpp}
% \fmfshift{0.14 (vloc ip - vloc vp)}{vpm}
% \fmf{plain}{ipp,vpp}
% \fmf{plain}{ipm,vpm}
% \fmfblob{.15w}{vp}
% \fmfdot{vq}
% \end{fmfchar}
% \end{center}
% \end{minipage}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Loose arcs}
%
% Adding arcs \emph{after} any |\fmfposition| involving these
% vertices will make these arcs loose, i.e.~they will not contribute
% to the bonding between the vertices.
%
% Consider the following example: suppose we want to draw a ladder
% diagram contributing to the quark form factor. Simply linking in
% the gluons does not produce a satisfactory result:
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{i1} \fmfoutgoing{o1,o2}
% \fmf{photon}{i1,v4}
% \fmf{quark}{o1,v1,v2,v3,v4,v5,v6,v7,o2}
% \fmf{gluon}{v1,v7}
% \fmf{gluon}{v2,v6}
% \fmf{gluon}{v3,v5}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.35\linewidth}
% \begin{center}
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \fmfincoming{i1} \fmfoutgoing{o1,o2}
% \fmf{photon}{v4,i1}
% \fmf{quark}{o1,v1,v2,v3,v4,v5,v6,v7,o2}
% \fmf{gluon}{v1,v7}
% \fmf{gluon}{v2,v6}
% \fmf{gluon}{v3,v5}
% \end{fmfchar}
% \end{center}
% \end{minipage}
%
% What went wrong? Obviously the gluons are bonding the quark lines
% too strongly. The fix is simple: just exclude the gluons from the
% calculation and add them later as infinitely stretchable:
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{i1} \fmfoutgoing{o1,o2}
% \fmf{photon}{i1,v4}
% \fmf{quark}{o1,v1,v2,v3,v4,v5,v6,v7,o2}
% \fmfposition
% \fmf{gluon}{v1,v7}
% \fmf{gluon}{v2,v6}
% \fmf{gluon}{v3,v5}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.35\linewidth}
% \begin{center}
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \fmfincoming{i1} \fmfoutgoing{o1,o2}
% \fmf{photon}{v4,i1}
% \fmf{quark}{o1,v1,v2,v3,v4,v5,v6,v7,o2}
% \fmfposition
% \fmf{gluon}{v1,v7}
% \fmf{gluon}{v2,v6}
% \fmf{gluon}{v3,v5}
% \end{fmfchar}
% \end{center}
% \end{minipage}
%
% Another instructive example is the following: imagine you want to
% draw a typical non-resonant contribution to~$e^+e^-\to 4f$. The
% obvious solution doesn's look right.
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmf{fermion}{i1,v1,i2}
% \fmf{photon}{v1,v2}
% \fmf{fermion}{o1,v2,v3,o4}
% \fmf{photon}{v3,v4}
% \fmf{fermion}{o3,v4,o2}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.35\linewidth}
% \begin{center}
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmf{fermion}{i1,v1,i2}
% \fmf{photon}{v1,v2}
% \fmf{fermion}{o1,v2,v3,o4}
% \fmf{photon}{v3,v4}
% \fmf{fermion}{o3,v4,o2}
% \end{fmfchar}
% \end{center}
% \end{minipage}
%
% One way to fix it is to |\fmfshift| the three rightmost vertices by
% hand:
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmf{fermion}{i1,v1,i2}
% \fmf{photon}{v1,v2}
% \fmf{fermion}{o1,v2,v3,o4}
% \fmf{photon}{v3,v4}
% \fmf{fermion}{o3,v4,o2}
% \fmfposition
% \fmfshift{-.1w,0}{v2,v3,v4}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.35\linewidth}
% \begin{center}
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmf{fermion}{i1,v1,i2}
% \fmf{photon}{v1,v2}
% \fmf{fermion}{o1,v2,v3,o4}
% \fmf{photon}{v3,v4}
% \fmf{fermion}{o3,v4,o2}
% \fmfposition
% \fmfshift{-.1w,0}{v2,v3,v4}
% \end{fmfchar}
% \end{center}
% \end{minipage}
%
% A smarter solution is again to make certain arcs stretchable:
% \vspace*{\baselineskip}
%
% \begin{minipage}{0.6\linewidth}
% \begin{verbatim}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmf{fermion}{i1,v1,i2}
% \fmf{photon}{v1,v2}
% \fmf{fermion}{o1,v2,v3,o4}
% \fmfposition
% \fmf{photon}{v3,v4}
% \fmf{fermion}{o3,v4,o2}
% \end{verbatim}
% \end{minipage}
% \hfill
% \begin{minipage}{0.35\linewidth}
% \begin{center}
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \fmfincoming{i1,i2}
% \fmfoutgoing{o1,o2,o3,o4}
% \fmf{fermion}{i1,v1,i2}
% \fmf{photon}{v1,v2}
% \fmf{fermion}{o1,v2,v3,o4}
% \fmfposition
% \fmf{photon}{v3,v4}
% \fmf{fermion}{o3,v4,o2}
% \end{fmfchar}
% \end{center}
% \end{minipage}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Avoiding continuously tight and loose}
%
% I have been very reluctant to implement continuously tight and loose
% arcs in \FMF, because it introduces to much opportunity for
% ``fiddling'' on the user's part. However, since the present
% implementation blends rather nicely with the options syntax, I have
% decided to add it anyway. I hope that most diagrams will be created
% without too much ``fiddling''.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Raw \MF}
%
% Some more advanced features of \FMF{} are more conveniently
% accessed through raw \MF{} commands. This can either be
% achieved by preparing a \MF{} input file or by using |\fmfcmd|
% extensively. The latter apprach is usally more convenient.
%
% \DescribeMacro{\fmfcmd}
% The |\fmfcmd| macro writes its argument into the \MF{} input
% file generated by \FMF. While some experience in using
% \MF{} doesn't hurt here, this approach can simplify the
% production of complex diagrams considerably.
%
% An advanced application of the \MF{} features is shown in
% figure~\ref{fig:euler-heisenberg}, which is generated by calling
% the \TeX{} macro
% \begin{verbatim}
% \def\EulerHeisenberg#1{%
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \fmfcmd{vsurroundn (e,#1);}
% \fmfcmd{for n = 1 upto #1: vconnect ("photon", e[n], i[n]); endfor}
% \fmfcmd{vcycle ("fermion,tension=#1/8", i, #1);}
% \end{fmfchar}}
% \end{verbatim}
% with the arguments 4, 6, 8, and 10, respectively. These features
% are currently not
% available from \TeX, \MF{} has to be called explicitely through
% |\fmfcmd|.
% \def\EulerHeisenberg#1{%
% \begin{fmfchar}(40,25)
% \fmfpen{thick}
% \fmfcmd{vsurroundn (e,#1);}
% \fmfcmd{for n = 1 upto #1: vconnect ("photon", e[n], i[n]); endfor}
% \fmfcmd{vcycle ("fermion,tension=#1/8", i, #1);}
% \end{fmfchar}}
% \begin{figure}
% \begin{center}
% \EulerHeisenberg{4} \qquad \EulerHeisenberg{6}
% \end{center}
% \begin{center}
% \EulerHeisenberg{8} \qquad \EulerHeisenberg{10}
% \end{center}
% \caption{Higher order terms in the Euler-Heisenberg lagrangian.}
% \label{fig:euler-heisenberg}
% \end{figure}
%
% Finally, for the curious, here is how to draw the circular gluons in
% figure~\ref{fig:gluons}:
% \begin{verbatim}
% \fmfcmd{draw_gluon (fullcircle scaled .5w shifted (.5w,.5h));}
% \fmfcmd{draw_gluon (reverse fullcircle scaled .5w shifted (.5w,.5h));}
% \end{verbatim}
%
% \begin{figure}
% \begin{center}
% \begin{fmfchar}(40,40)
% \fmfcmd{draw_gluon (fullcircle scaled .5w shifted (.5w,.5h));}
% \end{fmfchar}
% \qquad
% \begin{fmfchar}(40,40)
% \fmfcmd{draw_gluon (reverse fullcircle scaled .5w shifted (.5w,.5h));}
% \end{fmfchar}
% \end{center}
% \caption{Circular gluons.}
% \label{fig:gluons}
% \end{figure}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Limitations}
%
% Currently the most severe limitation lies in the size of the
% generated pictures. The largest number \MF{} can represent
% internally is~4095.99998 and this is also the largest value any
% coordinate measured in pixels can assume. At the most popular
% laserprinter resolution of~300 dots per inch (dpi), this corresponds
% to a horizontal and vertical extension of about~346mm, which is
% plenty and we're more likely to hit the internal limits on the
% complexity of a picture. However, at the proof mode resolution
% of~2601.72dpi, this is reduced to slightly less than~40mm and we're
% running the risk of arithmetic overflow in internal calculations much
% earlier.
%
% There are two potential solutions of different scope and complexity:
% \begin{itemize}
% \item{} Once John Hobby's \MP{} is available without a
% non-disclosure agreement, a solution is to replace \MF{} by
% \MP, which doesn't suffer from the size
% limitations\footnote{%
% Right now, \FMF's \MP{} support is still
% somewhat kludged, but the functionality is there.}
% This comes with a small price paid in reduced portability of the
% generated output, but as already stated above in the case of
% |axodraw|, the ubiquity of PostScript printers (and the free
% GhostScript interpreter) makes this a minor point.
% \item{} The more ambitious solutions will be ``virtual pictures''
% (see section~\ref{sec:virtual-pictures}).
% \end{itemize}
%
% \end{fmffile}
%
% \StopEventually{}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{\TeX{} macros}
%
% It's is good practice to identify this version of the document style
% option. We do this by parsing an RCS |Id| string and storing the
% result in the conventional \TeX{} control sequences:
% \changes{1.1}{1994/05/19}{%
% Don't loose on {\tt RCS} strings even iff the dollar signs have
% been removed.}
% \begin{macrocode}
%<*style>
\NeedsTeXFormat{LaTeX2e}
{\def\RCS#1#2\endRCS{%
\ifx$#1%
\@RCS $#2 \endRCS
\else
\@RCS $*: #1#2$ \endRCS
\fi}%
\def\@RCS $#1: #2,v #3 #4 #5 #6$ \endRCS{%
\gdef\filename{#2}%
\gdef\fileversion{v#3}%
\gdef\filedate{#4}%
\gdef\docdate{#4}}%
\RCS feynmf.dtx,v 1.5 1994/05/28 12:10:04 ohl Exp \endRCS}%
% \end{macrocode}
%
% And now the standard procedure:
% \changes{1.4}{1994/05/27}{%
% \MP{} support: identification part, include
% \texttt{egraphics} and pass options.}
% \begin{macrocode}
%<*!mp>
\ProvidesPackage{feynmf}[\filedate\space LaTeX2e package]
\typeout{Package: `feynmf'
\fileversion\space <\filedate> (tho) PRELIMINARY TEST RELEASE}
\wlog{English documentation \@spaces<\docdate> (tho)}
%
%<*mp>
\ProvidesPackage{feynmp}[\filedate\space LaTeX2e package]
\typeout{Package: `feynmp'
\fileversion\space <\filedate> (tho) PRELIMINARY TEST RELEASE}
\wlog{English documentation \@spaces<\docdate> (tho)}
% \end{macrocode}
% Every option we don't understand (that is \emph{every} option) is
% sent down to |egraphics|:
% \begin{macrocode}
\DeclareOption*{\PassOptionsToPackage{\CurrentOption}{egraphics}}
\ProcessOptions
% \end{macrocode}
% For the sake of Portabilitical Correctness, we use \LaTeX's
% |egraphics| for including PostScript, instead of the simpler |epsf|
% which comes with |dvips| and would have sufficed
% \begin{macrocode}
\RequirePackage{egraphics}
%
% \end{macrocode}
%
% \begin{dubious}
% We should |\||mdqon| at the end only if the German extensions are
% really active, not just loaded.
% \end{dubious}
% \begin{macrocode}
\let\mdqrestore\relax
\@ifundefined{mdqoff}{}{%
\mdqoff
\let\mdqrestore\mdqon}
% \end{macrocode}
%
% \begin{macro}{\fmfcmd}
% The entrance through which our commands enter the world of
% \MF. Note the |\ignorespaces|: we need to avoid spurious
% blanks in the output list.
% \begin{macrocode}
\newwrite\@outfmf
\def\fmfcmd#1{%
\immediate\write\@outfmf{#1}\ignorespaces}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmffile}
% This environment encloses each \MF{} input file. The single
% argument gives the name of the file.
% \changes{1.1}{1994/05/16}{%
% Stupid: {\tt fileversion} can be reset by other packages, store
% the current value in {\tt fmf@fileversion} and use this one.}
% \changes{1.1}{1994/05/20}{%
% Pass RCS revision in a string.}
% \changes{1.4}{1994/05/27}{\MP{} support: write \MP{} file.}
% \begin{macrocode}
{\catcode`\%=11\gdef\p@rcent{%}}
\edef\fmf@fileversion{\fileversion}
\def\fmffile#1{%
\def\thefmffile{#1}%
%<*!mp>
\immediate\openout\@outfmf=\thefmffile.mf\relax
\fmfcmd{\p@rcent\space \thefmffile.mf -- do not edit, %
generated automatically by \jobname.tex^^J%
input feynmf^^J%
\p@rcent\space tracingonline:=tracingtitles:=1;^^J%
require_RCS_revision "\expandafter\@gobble\fmf@fileversion";}%
%
%<*mp>
\immediate\openout\@outfmf=\thefmffile.mp\relax
\fmfcmd{\p@rcent\space \thefmffile.mp -- do not edit, %
generated automatically by \jobname.tex^^J%
input feynmp^^J%
\p@rcent\space tracingonline:=tracingtitles:=1;^^J%
require_RCS_revision "\expandafter\@gobble\fmf@fileversion";}%
%
% \end{macrocode}
% The following trick has been taken from |mfpic|~\cite{mfpic}:
% proceed even if the font is not available yet, because we have to
% write the \MF{} file first.
% \changes{1.4}{1994/05/27}{\MP{} support: don't open \texttt{tfm} file.}
% \begin{macrocode}
%<*!mp>
\batchmode
\font\f@ynmf=\thefmffile
\errorstopmode
% \end{macrocode}
% Inform the user:
% \begin{macrocode}
\ifx\f@ynmf\nullfont
\def\f@ynmf{feynmf character:}%
\typeout{%
feynmf: File \thefmffile.tfm not found:^^J%
feynmf: Process \thefmffile.mf with METAFONT and then %
reprocess this file.}%
\else
\typeout{%
feynmf: File \thefmffile.tfm found.^^J%
feynmf: Nevertheless, if the picture has changed, %
reprocess \thefmffile.mf.^^J%
feynmf: If dimension have changed, reprocess \thefmffile.mf %
and \jobname.tex.}%
\fi
%
% \end{macrocode}
% Count the characters
% \begin{macrocode}
\setcounter{fmfchar}{0}}
\let\thefmffile\relax
\newcounter{fmfchar}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\endfmffile}
% And here is how we close the |fmffile| environment:
% \begin{macrocode}
\def\endfmffile{%
\fmfcmd{\p@rcent\space the end.^^J%
end.^^J%
endinput;}%
\let\thefmffile\relax
\immediate\closeout\@outfmf}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmf@char}
% This is the bulk of the environment used for each ``character''
% drawn by \MF.
% \begin{macrocode}
{\catcode`\#=11\gdef\sh@rp{#}}
\let\sharp\sh@rp
\def\fmf@char#1#2{%
% \end{macrocode}
% Make sure that a \MF{} file is open, otherwise \emph{really}
% obscure error messages are possible:
% \changes{1.3}{1994/05/23}{%
% Make sure that a \MF{} file is open, otherwise \emph{really}
% obscure error messages are possible.}
% \begin{macrocode}
\ifx\thefmffile\relax
\errhelp={Outside a fmffile environment, I have no clue as to where^^J%
the METAFONT commands should go. I will use fmfdeflt.mf^^J%
for this character, but you'd better fix your code!}
\errmessage{I detected a fmfchar environment outside of fmffile}
\fmffile{fmfdeflt}
\fi
\stepcounter{fmfchar}%
% \end{macrocode}
% Start \MF{} character:
% \begin{macrocode}
\fmfcmd{beginchar(\thefmfchar, #1*\the\unitlength\sh@rp, %
#2*\the\unitlength\sh@rp, 0);^^J%
"feynmf: \thefmfchar";}%
\fmfcmd{LaTeX_unitlength:=\the\unitlength;}%
\fmfinit
\fmfpen{thin}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmfchar}
% The plain version, no labels, no enclosing |picture| environment
% \begin{macrocode}
\def\fmfchar(#1,#2){%
\fmf@char{#1}{#2}%
% \end{macrocode}
% Place the character:
% \changes{1.4}{1994/05/27}{\MP{} support: include PostScript file.}
% \begin{macrocode}
%{\f@ynmf \char\value{fmfchar}}%
%<*mp>
\leavevmode
\IfFileExists{\thefmffile.\thefmfchar}%
{\includegraphics[type=eps,ext=\thefmfchar,read=\thefmfchar]%
{\thefmffile}}%
{\typeout{%
feynmp: File \thefmffile.\thefmfchar\space not found:^^J%
feynmp: Process \thefmffile.mf with MetaPost and then %
reprocess this file.}}%
%
\ignorespaces}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\endfmfchar}
% \begin{macrocode}
\def\endfmfchar{%
\fmfposition
\fmfdraw
\fmfcmd{endchar;}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmfchar*}
% The extended version, with labels and |picture| environment.
% \begin{macrocode}
\@namedef{fmfchar*}(#1,#2){%
\begin{picture}(#1,#2)
\fmf@char{#1}{#2}%
% \end{macrocode}
% Process the \MF{} output for labels (if any), enforcing |%| as
% comment character.
% \begin{macrocode}
%<*!mp>
{\catcode`\%=14\relax
\grepfile{%
\thefmffile.\thefmfchar}{%
\thefmffile.log}{%
\thefmffile.t\thefmfchar}}%
%
% \end{macrocode}
% Place the character:
% \changes{1.4}{1994/05/27}{\MP{} support: include PostScript file.}
% \begin{macrocode}
%\put(0,0){{\f@ynmf \char\value{fmfchar}}}%
%<*mp>
\IfFileExists{\thefmffile.\thefmfchar}%
{\put(0,0){\includegraphics[type=eps,ext=\thefmfchar,read=\thefmfchar]%
{\thefmffile}}}%
{\typeout{%
feynmp: File \thefmffile.\thefmfchar\space not found:^^J%
feynmp: Process \thefmffile.mf with MetaPost and then %
reprocess this file.}}%
%
\ignorespaces}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\endfmfchar*}
% \begin{macrocode}
\@namedef{endfmfchar*}{%
\endfmfchar
% \end{macrocode}
% Enforce |%| as comment character:
% \begin{macrocode}
{\catcode`\%=14\relax
\InputIfFileExists{\thefmffile.t\thefmfchar}{}{%
\typeout{%
feynmf: Label file \thefmffile.t\thefmfchar\space not found:^^J%
feynmf: Process \thefmffile.mf with METAFONT and then %
reprocess this file.}}}%
\end{picture}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmfframe}
% This is used to allocate additional space around a |fmfchar*|, since
% the labels (or the diagram itself) might overshoot.
% |\fmfchar(|\meta{left}|,|\meta{top}|)(|\meta{right}|,|\meta{bottom}|){|%
% \meta{box}|}| puts an invisible frame of the given dimensions
% (measured in |\unitlength|) around \meta{box}.
% \begin{macrocode}
\def\fmfframe(#1,#2)(#3,#4)#5{%
\leavevmode
\hbox{\vbox{\vskip#2\unitlength\par
\hbox{\hskip#1\unitlength#5\hskip#3\unitlength}\par
\vskip#4\unitlength}}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmfpen}
% Picup a |pencircle| scaled by the argument.
% \begin{macrocode}
\def\fmfpen#1{\fmfcmd{pickup pencircle scaled #1;}}
% \end{macrocode}
% \end{macro}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Grep}
% \label{sec:grep}
%
% \begin{macro}{\grepfile}
% The macro |\grepfile{|\meta{pattern}|}{|\meta{in}|}{|\meta{out}|}|
% writes all lines matching |:|\meta{pattern}|:| from file \meta{in}
% to file \meta{out} after stripping off the pattern.
% \begin{dubious}
% Pattern matching on lines with a single leading colon fails.
% \end{dubious}
% \changes{1.4}{1994/05/28}{%
% Don't include the \texttt{grep} macros in the \MP{} version.
% \texttt{write} makes them obsolete.}
% \begin{macrocode}
%<*!mp>
\def\grepfile#1#2#3{%
\begingroup
% \end{macrocode}
% Hash the pattern and open the input and output streams:
% \begin{macrocode}
\edef\pattern{\csname*grep*#1*\endcsname}%
\immediate\openin\grep@infile #2\relax
\ifeof\grep@infile
\else
\grep@outopenfalse
% \end{macrocode}
% Don't add anything at the end of input lines and don't expand
% anything we've read from the file:
% \begin{macrocode}
\endlinechar=-1
\catcode`\\=12\relax
% \end{macrocode}
% Loop over the input lines until end of file occurs:
% \begin{macrocode}
\loop
\read\grep@infile to \grep@lbuf
\ifeof\grep@infile
\grep@contfalse
\else
\grep@conttrue
% \end{macrocode}
% Iff the input line is not empty, use |\grep@aline| to examine its
% contents and, iff the pattern matched, write a line to the output file.
% \begin{macrocode}
\ifx\grep@lbuf\empty
\else
\expandafter\grep@aline\grep@lbuf\sentinel
\ifx\pattern\grep@tag
% \end{macrocode}
% Delayed open (this avoids empty files):
% \begin{macrocode}
\ifgrep@outopen
\else
\immediate\openout\grep@outfile #3\relax
\immediate\write\grep@outfile{\p@rcent\space #3 %
-- generated automatically from #2}%
\immediate\write\grep@outfile{\p@rcent\space
Think twice before editing THIS file!}%
\grep@outopentrue
\fi
\immediate\write\grep@outfile{\grep@val}%
\fi
\fi
\fi
\ifgrep@cont
\repeat
% \end{macrocode}
% Close the files after we're done.
% \changes{1.1}{1994/05/16}{%
% Stupid: {\tt closein} the input stream, don't use {\tt closeout} on it.}
% \begin{macrocode}
\ifgrep@outopen
\immediate\closeout\grep@outfile
\fi
\fi
\immediate\closein\grep@infile
\endgroup}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\grep@infile}
% \begin{macro}{\grep@outfile}
% The I/O streams for the grep facility
% \begin{macrocode}
\newread\grep@infile
\newwrite\grep@outfile
% \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\ifgrep@cont}
% \begin{macro}{\ifgrep@outopen}
% and flags for the same
% \begin{macrocode}
\newif\ifgrep@cont
\newif\ifgrep@outopen
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\grep@aline}
% Examine one line and set the variables |\grep@tag| and |\grep@val|
% iff the line starts with a colon. Subtle point here: |\ifx#1:| will
% \emph{not} work if |#1| starts with a |{| followed by two identical
% characters.
% \begin{macrocode}
\def\grep@aline#1#2\sentinel{%
\ifx:#1%
\grep@splitlbuf#2\sentinel
\else
\edef\grep@tag{\csname*grep*\endcsname}%
\def\grep@val{}%
\fi}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\grep@splitlbuf}
% Split the line buffer at the remaining colon, hashing the first part.
% \begin{macrocode}
\def\grep@splitlbuf#1:#2\sentinel{%
\edef\grep@tag{\csname*grep*#1*\endcsname}%
\def\grep@val{#2}}
%
% \end{macrocode}
% \end{macro}
%
% The other \TeX{} command sequences are defined below, along with the
% \MF{} macros they are in one-to-one correspondence to.
% \begin{macrocode}
%
% \end{macrocode}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{\MF{} macros}
% \label{sec:mf-code}
%
% Now we turn our attention to the \MF{}
% macros.
% \begin{dubious}
% We should find a way (a hack) to index the
% \MF{} macros with the |doc| option.
% \end{dubious}
% Make the RCS revision number available for feature testing:
% \changes{1.1}{1994/05/20}{%
% Handle arbitrary RCS revision strings.}
% \begin{macrocode}
%<*base>
vardef parse_RCS (suffix RCS) (expr s) =
save n, c;
numeric n, RCS[];
string c;
RCS[0] := 0;
for n = 1 upto length (s):
c := substring (n-1,n) of s;
exitif ((RCS[0] > 0) and (c = " "));
if ((c = "0") or (c = "1") or (c = "2")
or (c = "3") or (c = "4") or (c = "5")
or (c = "6") or (c = "7") or (c = "8")
or (c = "9")):
if RCS[0] = 0:
RCS[0] := 1;
RCS[RCS[0]] := 0;
fi
RCS[RCS[0]] := 10 * RCS[RCS[0]] + scantokens (c);
elseif c = ".":
RCS[0] := RCS[0] + 1;
RCS[RCS[0]] := 0;
else:
fi
endfor
enddef;
% \end{macrocode}
% Check that \LaTeX{} style and \MF{} macros are in sync:
% \begin{macrocode}
vardef require_RCS_revision expr s =
numeric n;
save TeX_rev, mf_rev;
parse_RCS (TeX_rev, s);
parse_RCS (mf_rev, "1.5");
for n = 1 upto min (2, TeX_rev[0], mf_rev[0]):
if TeX_rev[n] > mf_rev[n]:
errhelp
"Your version of `feynmf.sty' is higher that of your `feynmf.mf'.";
errmessage "feynmf: Metafont macros out of date";
elseif TeX_rev[n] < mf_rev[n]:
errhelp
"Your version of `feynmf.mf' is higher that of your `feynmf.sty'.";
errmessage "feynmf: LaTeX style out of date";
fi
exitif (TeX_rev[n] <> mf_rev[n]);
endfor
enddef;
% \end{macrocode}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{\MP{} Kludges}
%
% This is not \MP{} support yet, just trying to prove a point.
% \changes{1.4}{1994/05/27}{Preliminary \MP{} support: mimic \MF.}
% \begin{macrocode}
%<*mp>
vardef cullit = \ enddef;
% \end{macrocode}
%
% \begin{macrocode}
vardef beginchar (expr c, wd, ht, dp) =
LaTeX_file := "";
beginfig(c);
w:=wd;
h:=ht;
enddef;
string LaTeX_file;
% \end{macrocode}
%
% \begin{macrocode}
vardef endchar =
setbounds currentpicture to (0,0)--(w,0)--(w,h)--(0,h)--cycle;
if LaTeX_file <> "":
write EOF to LaTeX_file;
LaTeX_file := "";
fi
endfig
enddef;
% \end{macrocode}
%
% Sharped dimensions are useless with \MP. We define them anyway
% with trivial translation, so that the \MF{} code can be used
% unchanged.
% \begin{macrocode}
bp# := bp;
cc# := cc;
cm# := cm;
dd# := dd;
in# := in;
mm# := mm;
pc# := pc;
pt# := pt;
% \end{macrocode}
% As I said: trivial translation.
% \begin{macrocode}
vardef define_blacker_pixels(text t) =
forsuffixes $=t:
$:=$.#;
endfor
enddef;
%
% \end{macrocode}
%
% \begin{macrocode}
%mode_setup;
% \end{macrocode}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Basics}
% \label{sec:mf-basics}
%
% Default values of style parameters:
% \begin{macrocode}
thin#:=1pt#; % dimension of the lines
thick#:=2thin#;
arrow_width#:=3thick#; % arrows
arrow_height#:=2arrow_width#;
curly_len#:=3mm#;
dash_len#:=3mm#; % 'photon' lines
dot_len#:=2mm#; % 'photon' lines
wiggly_len#:=4mm#; % 'photon' lines
wiggly_slope:=60;
shade_black#:=1pt#; % shading
shade_white#:=2shade_black#;
shade_angle:=60;
% \end{macrocode}
% Convert ``sharp'' units:
% \begin{macrocode}
define_blacker_pixels (thick, thin, shade_black, shade_white,
dash_len, dot_len, wiggly_len, curly_len,
arrow_height, arrow_width);
% \end{macrocode}
%
% Default to metric units, but this will be reset by |\begin{fmfchar}|
% anyway.
% \begin {macrocode}
LaTeX_unitlength := mm;
% \end{macrocode}
%
% Count the number of tokens in the argument:
% \begin {macrocode}
vardef count (text list) =
forsuffixes $ = list: + 1 endfor
enddef;
% \end{macrocode}
%
% Parse the string |s| into comma separated tokens |opt[]|, ignoring
% blanks before |=|'s. Double commas are passed as a single comma.
% \begin {macrocode}
vardef getopt (suffix opt) (expr s) =
numeric opt.first, opt.last, n;
string opt[], opt[]arg, c;
boolean argp, escape;
opt.first := 0;
opt.last := 0;
opt[opt.last] := "";
argp := false;
escape := false;
for n = 1 upto length (s):
c := substring (n-1,n) of s;
% \end{macrocode}
% If we see a comma which has not been escaped, check for a second
% comma and set the |escape| flag or reset the |argp| flag, as
% appropriate:
% \begin {macrocode}
if not escape and (c = ","):
if substring (n,n+1) of s = ",":
escape := true;
else:
opt.last := opt.last + 1;
opt[opt.last] := "";
argp := false;
fi
% \end{macrocode}
% Start as argument and ignore |=|'s until the next option:
% \begin {macrocode}
elseif not argp and (c = "="):
opt[opt.last]arg := "";
argp := true;
% \end{macrocode}
% Accept the next character (either option or argument) and reset the
% |escape| flag:
% \begin {macrocode}
elseif argp or (c <> " "):
if argp:
opt[opt.last]arg := opt[opt.last]arg & c;
else:
opt[opt.last] := opt[opt.last] & c;
fi
escape := false;
fi
endfor
enddef;
% \end{macrocode}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Manipulating \texttt{picture}s}
% \label{sec:pictures}
%
% |save_picture (list_of_pictures)| |save|'s each member of
% |list_of_pictures| inside a group and reinitializes them as nullpictures.
% \begin{macrocode}
def save_picture text t =
save t; picture t; forsuffixes p=t: p:=nullpicture; endfor
enddef;
% \end{macrocode}
%
% |begin_sketch| pushes the sketchpad stack and perform the following
% drawing commands (upto the next |end_sketch|) on the new sketchpad.
% \begin{macrocode}
def begin_sketch =
begingroup save_picture currentpicture;
sketchlevel := sketchlevel+1;
enddef;
% \end{macrocode}
%
% |end_sketch| pops the sketchpad stack.
% \begin{macrocode}
def end_sketch =
sketchlevel := sketchlevel-1;
sketchpad[sketchlevel] := currentpicture;
endgroup
enddef;
%
picture sketchpad[];
sketchlevel := 1;
% \end{macrocode}
%
% |use_sketch (transformation)| copies the transformed sketchpad into
% the current picture.
% \begin{macrocode}
vardef use_sketch text t =
addto currentpicture also (sketchpad[sketchlevel] t)
enddef;
% \end{macrocode}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Shading}
% \label{sec:shading}
%
% |shade (path_arg)| shades the interior of |path_arg|. This shading is
% controlled by the global variables |shade_black|, |shade_white|, and
% |shade_angle|.
% Caveat: The procedure is only guaranteed to work for convex paths.
% \begin{dubious}
% \MP{} has nice primitives to aid in finding bounding boxes, in
% \MF{} we have to rely on heuristics.
% \end{dubious}
% \begin{macrocode}
vardef shade expr p_arg =
save x,y,d,p,currentpen; path p; pen currentpen; % push pen!
pickup pencircle scaled shade_black;
p = p_arg rotated - shade_angle; % calculate enclosing rectangle
x2' = x3' = xpart directionpoint up of p; % (rotated by |shade_angle|).
x1' = x4' = xpart directionpoint down of p;
y1' = y2' = ypart directionpoint right of p;
y3' = y4' = ypart directionpoint left of p;
forsuffixes $=1,2,3,4: z$ = z$' rotated shade_angle; endfor
d = abs(z1-z4); % height.
begin_sketch % fill rectangle with lines.
for k=shade_white/d step (shade_white+shade_black)/d
until 1 - shade_white/d:
cutdraw k[z1,z4] -- k[z2,z3];
endfor
% \end{macrocode}
% \MF{} has no clipping operation, but since we know the bounding box,
% we can use \MF's pixel arithmetic for calculating the set
% theoretical intersection of the interior of |p_arg| and the diagonal
% lines in the bounding box:
% \begin{macrocode}
%<*!mp>
cullit;
fill p_arg;
unfill z1--z2--z3--z4--cycle;
cullit;
%
% \end{macrocode}
% \MP{} has clipping build in but no pixel arithmetic:
% \changes{1.4}{1994/05/28}{\MP{} support: shading.}
% \begin{macrocode}
%<*mp>
clip currentpicture to p_arg;
%
end_sketch;
use_sketch;
enddef;
% \end{macrocode}
%
% \begin{dubious}
% Fix the placement of arrows on curved arcs. John Hobby has a
% particulary nice idea in plain \MP.
% \end{dubious}
% |arrow| expands to the standard arrowhead for fermions etc.
% \begin{macrocode}
vardef arrow =
clearxy; % push 'em!
x1 - x2 = arrow_height; y2 - y3 = arrow_width;
x1 = -3x2; x2 = x3; y1 = y2 + y3 = 0; % center it!
z1--z2--z3--cycle
enddef;
% \end{macrocode}
%
% |cut_circles| expands to a subpath of |path_arg|, excluding circles of
% |diam_a| (resp. |diam_b|) centered at the beginning (resp.~end) of
% |path_arg|.
% \begin{macrocode}
vardef cut_circles (expr diam_a, p_arg, diam_b) =
subpath (xpart(p_arg intersectiontimes fullcircle scaled diam_a
shifted point 0 of p_arg),
xpart(p_arg intersectiontimes fullcircle scaled diam_b
shifted point infinity of p_arg))
of p_arg
enddef;
% \end{macrocode}
%
% The function |make_blob| is the working horse of |draw_blob|.
% \begin{macrocode}
vardef make_blob (expr z_arg, diameter) =
save p,currentpen; path p; pen currentpen;
pickup pencircle scaled thick;
p = fullcircle scaled diameter shifted z_arg;
draw p; shade p;
enddef;
% \end{macrocode}
%
% |draw_blob (pair_arg, diameter)| draws a shaded blob of diameter
% |diameter| centered at |pair_arg|. The thickness of the border is
% controlled by the global variable |thick|.
%
% Hint: It saves time to draw blobs of the same size in sequence.
% \begin{macrocode}
vardef draw_blob (expr z_arg, diameter) =
if sketched_blob_diameter <> diameter: % drawn lately?
begin_sketch make_blob (origin, diameter); end_sketch; % redo hard work!
sketched_blob_diameter:= diameter; % record it
fi
use_sketch shifted z_arg; % the easy way ...
enddef;
% \end{macrocode}
%
% |force_new_blob| forces the redrawing of a blob of the same diameter
% (in case you only changed the shading parameters).
% \begin{macrocode}
def force_new_blob = sketched_blob_diameter := -1; enddef;
force_new_blob; % initialize it.
% \end{macrocode}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Drawing}
% \label{sec:drawing}
%
% |put_on_path (object, path_arg)| returns the |path_arg| after having
% drawn |object| (suitably rotated) at its mid point.
% \begin{macrocode}
vardef put_on_path (expr o_arg, p_arg) =
fill o_arg rotated angle direction length(p_arg)/2 of p_arg
shifted point length(p_arg)/2 of p_arg;
p_arg
enddef;
% \end{macrocode}
%
% Easier than
% \begin{equation}
% \int_0^1 dt \left\vert\frac{dx(t)}{dt}\right\vert
% \end{equation}
% with the integrand the square root of a fourth order polynomial, but
% sufficient for all practical purposes is
% \begin{macrocode}
vardef pixlen (expr p, n) =
for k=1 upto length(p): + segment_pixlen (subpath (k-1,k) of p, n) endfor
enddef;
% \end{macrocode}
%
% \begin{macrocode}
vardef segment_pixlen (expr p, n) =
for k=1 upto n: + abs (point k/n of p - point (k-1)/n of p) endfor
enddef;
% \end{macrocode}
%
% |wiggly (path_arg)| expands to a ``wiggled'' version of |path_arg|. The
% slope of the wiggles is controlled by the global variable |wiggle_slope|,
% the length of the wiggles by the global variable |wiggly_len|.
% \begin{macrocode}
vardef wiggly (expr p_arg) =
numeric wpp;
wpp := ceiling (pixlen (p_arg, 10) / (wiggly_len * length(p_arg)));
for k=0 upto wpp*length(p_arg) - 1:
point k/wpp of p_arg
{direction k/wpp of p_arg rotated wiggly_slope} ..
point (k+.5)/wpp of p_arg
{direction (k+.5)/wpp of p_arg rotated - wiggly_slope} ..
endfor
if cycle p_arg: cycle else: point infinity of p_arg fi
enddef;
% \end{macrocode}
%
% |curly (path_arg)| expands to a ``curly'' version of |path_arg|. The
% the length of the curls is controlled by the global variable
% |curly_len|.
% \begin{macrocode}
vardef curly (expr p_arg) =
numeric cpp;
cpp := ceiling (pixlen (p_arg, 10) / (curly_len * length(p_arg)));
if cycle p_arg:
for k=0 upto cpp*length(p_arg) - 1:
point (k+.33)/cpp of p_arg
{direction (k+.33)/cpp of p_arg rotated 90} ..
point (k-.33)/cpp of p_arg
{direction (k-.33)/cpp of p_arg rotated -90} ..
endfor
cycle
else:
point 0 of p_arg
{direction 0 of p_arg rotated -90} ..
for k=1 upto cpp*length(p_arg) - 1:
point (k+.33)/cpp of p_arg
{direction (k+.33)/cpp of p_arg rotated 90} ..
point (k-.33)/cpp of p_arg
{direction (k-.33)/cpp of p_arg rotated -90} ..
endfor
point infinity of p_arg
{direction infinity of p_arg rotated 90}
fi
enddef;
% \end{macrocode}
%
% |fermion (path_arg)| returns a fermion line (straight line with an arrow
% at the midpoint) on |path_arg|.
% |photon (path_arg)| returns a photon line (wiggled) on |path_arg|.
% \begin{macrocode}
vardef fermion expr path_arg = put_on_path (arrow, path_arg) enddef;
vardef photon expr path_arg = wiggly (path_arg) enddef;
vardef gluon expr path_arg = curly (path_arg) enddef;
% \end{macrocode}
%
% An inventory of valid line styles is implemented as a hash table:
% \begin{macrocode}
save vsty_hash;
% \end{macrocode}
% This is a bit like |mode_def| in plain \MF{} but doesn't use an
% array of available modes: |style_def "foo"| will define a macro
% |draw_foo| drawing a line of a certain style along any given path:
% \begin{macrocode}
def style_def suffix s =
vsty_hash.s := 1;
expandafter quote vardef scantokens ("draw_" & str s)
enddef;
% \end{macrocode}
%
% Let \MF{} do the lookup: suffices
% \begin{macrocode}
vardef vsty_exists suffix s =
known vsty_hash.s
enddef;
% \end{macrocode}
% an strings
% \begin{macrocode}
vardef valid_style expr s =
expandafter vsty_exists scantokens (s)
enddef;
% \end{macrocode}
%
% |phantom| lines are simple:
% \begin{macrocode}
style_def phantom expr path_arg = \ enddef;
% \end{macrocode}
% |plain| lines aren't harder and we allow |vanilla| as an alias:
% \begin{macrocode}
style_def plain expr p_arg = draw p_arg enddef;
style_def vanilla expr p_arg = draw p_arg enddef;
% \end{macrocode}
% And some more:
% \begin{macrocode}
style_def fermion (expr p_arg) = draw fermion (p_arg) enddef;
style_def quark (expr p_arg) = draw fermion (p_arg) enddef;
style_def electron (expr p_arg) = draw fermion (p_arg) enddef;
style_def photon (expr p_arg) = draw photon (p_arg) enddef;
style_def boson (expr p_arg) = draw photon (p_arg) enddef;
style_def gluon (expr p_arg) = draw gluon (p_arg) enddef;
% \end{macrocode}
% |draw_dashes (expr p_arg)| draws a scalar line (dashed line)
% on |path_arg|
% \changes{1.4}{1994/05/27}{%
% Rename the line style \texttt{dashed} to \texttt{dashes}, to avoid
% a name clash with \MP.}
% \begin{macrocode}
style_def dashes (expr p_arg) =
numeric dpp;
dpp := ceiling (pixlen (p_arg, 10) / (dash_len * length(p_arg)));
for k=0 upto dpp*length(p_arg) - 1:
draw point k/dpp of p_arg ..
point (k+.5)/dpp of p_arg;
endfor
enddef;
% \end{macrocode}
%
% \begin{macrocode}
style_def scalar (expr p_arg) =
draw_dashes (put_on_path (arrow, p_arg))
enddef;
% \end{macrocode}
%
% |draw_dots (expr p_arg)| draws a dotted line on |path_arg|
% \changes{1.4}{1994/05/27}{%
% Rename the line style \texttt{dotted} to \texttt{dots}, to be
% consistent with \texttt{dashes}.}
% \begin{macrocode}
style_def dots (expr p_arg) =
numeric dpp;
dpp := ceiling (pixlen (p_arg, 10) / (dot_len * length(p_arg)));
for k=0 upto dpp*length(p_arg):
drawdot point k/dpp of p_arg;
endfor
enddef;
% \end{macrocode}
%
% \begin{macrocode}
style_def ghost (expr p_arg) =
draw_dots (put_on_path (arrow, p_arg))
enddef;
% \end{macrocode}
%
% |draw_double (expr p_arg)| draws a double line.
% \begin{macrocode}
style_def double (expr p_arg) =
begingroup
pen oldpen;
oldpen := currentpen;
pickup oldpen scaled 3; % draw a thick linn
draw p_arg;
pickup oldpen;
cullit; undraw p_arg; cullit; % and remove the stuffing
endgroup;
enddef;
% \end{macrocode}
%
% |draw_heavy (expr p_arg)| draws a heavy line (double line with an
% arrow at the midpoint). |draw_double (fermion (..))| is an
% interesting alternative, but not very useful.
% \begin{macrocode}
style_def heavy (expr p_arg) =
begingroup
path discard;
draw_double (p_arg);
discard = fermion (p_arg);
endgroup
enddef;
% \end{macrocode}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Graphs of vertices}
% \label{sec:graphs}
%
% Here is the fun part of \FMF: \emph{automagic} placement of
% vertices.
% \begin{macrocode}
%tracingmacros:=1;
%tracingonline:=1;
tracingstats:=1;
% \end{macrocode}
%
% You can say |vtracing:=true| too see what's going on.
% \begin{macrocode}
boolean vtracing;
vtracing := false; % true
% \end{macrocode}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Data structures}
%
% \begin{table}
% \begin{tabular}{rll}
% Type & Name & Purpose \\\hline
% |numeric| & |vlist.first| & pointer to first vertex (usually 1) \\
% |numeric| & |vlist.last| & pointer to last vertex (starts with 0) \\
% |string| & |vlist[|$i$|]name| & symbolic name of the vertex\\
% |pair| & |vlist[|$i$|]loc| & position of the vertex \\
% |string| & |vlist[|$i$|]lbl| & label \\
% |numeric| & |vlist[|$i$|]lbl.ang| & angle \\
% |numeric| & |vlist[|$i$|]lbl.dist| & distance \\
% |numeric| & |vlist[|$i$|]arc.first| & pointer to first arc \\
% |numeric| & |vlist[|$i$|]arc.last| & pointer to last arc \\
% |numeric| & |vlist[|$i$|]arc[|$j$|]| & $j$th arc of the $i$th vertex \\
% |string| & |vlist[|$i$|]arc[|$j$|]sty| & style of the arc\\
% |numeric| & |vlist[|$i$|]arc[|$j$|]tns| & tension of the arc\\
% |string| & |vlist[|$i$|]arc[|$j$|]lsr| & left, straight, right\\
% |string| & |vlist[|$i$|]arc[|$j$|]lbl| & label\\
% |string| & |vlist[|$i$|]arc[|$j$|]lbl.side|& side of the label\\
% |numeric| & |vlist[|$i$|]arc[|$j$|]lbl.dist|& distance of the label\\
% |numeric| & |vlist[|$i$|]blob| & diameter of the ``blob''\\
% |numeric| & |vlist[|$i$|]dot| & whether to draw
% a dot at the vertex
% \end{tabular}
% \caption{Vertex data structure}
% \label{tab:VDS}
% \end{table}
% The data structure for our graph is shown in
% table~\ref{tab:VDS}\footnote{%
% \begin{dubious}
% \texttt{boolean vlist[i]arc[j]smooth} will indicate that this
% arc belongs to a set of arcs which are to be smoothly connected.
% The implementation will start by going to the strt of this set,
% define a long smooth path and finally do the drawing on the
% various subpaths.
% \end{dubious}}.
% \MF{} turns out to be quite powerful, providing such constructs
% in an unconventional, but flexible and concise way. While we use
% |save vhash| to forget all previously defined vertices, we leave
% |vlist| alone, because we will know from $|vlist.last| <
% |vlist.first|$ that it's empty. Note that we can't |vardef| this
% because then the |save| would go inside a group.
% \begin{macrocode}
def vinit =
save vhash;
numeric vlist.first, vlist.last;
vlist.first := 1;
vlist.last := 0;
pair vlist[]loc;
numeric vlist[]arc.first, vlist[]arc.last, vlist[]arc[],
vlist[]arc[]tns, vlist[]arc[]lbl.dist;
string vlist[]name, vlist[]lbl, vlist[]arc[]sty, vlist[]arc[]lsr,
vlist[]arc[]lbl, vlist[]arc[]lbl.side;
numeric vlist[]lbl.ang, vlist[]lbl.side, vlist[]blob, vlist[]dot;
enddef;
%
% \end{macrocode}
% \begin{macro}{\fmfinit}
% We can also ask for initialization explicitely from \TeX{} (usually
% it is called implicitely by |\begin{fmfchar}|). This flushes the
% vertex table.
% \begin{macrocode}
%
% \end{macrocode}
%
% \Finale
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{thebibliography}{99}
% \bibitem{TeX} Donald E.~Knuth, \textit{The \TeX{}book},
% Addison-Wesley, Reading, 1986.
% \bibitem{LaTeX} Leslie Lambort, \textit{\LaTeX{} --- A
% Documentation Preparation System},
% Addison-Wesley, Reading, 1985.
% \bibitem{LaTeX-Companion} Michel Goosens, Frank Mittelbach, and
% Alexander Samarin, \textit{The \LaTeX{} Companion},
% Addison-Wesley, Reading, 1994.
% \bibitem{MF} Donald E.~Knuth, \textit{The \MF{}book},
% Addison-Wesley, Reading, 1986.
% \bibitem{MetaPost} John D.~Hobby, \textit{A User's Manual for
% \MP}, Computer Science Report \#162, AT\&T Bell
% Laboratories, April 1992.
% \bibitem{hoenig} Alan Hoenig, \textit{When \TeX{} and \MF{}
% Work Together}, in \textit{Proceedings of the 7th European
% \TeX{} Conference, Prague}, p.~1, September 1992.
% \bibitem{levine} Micheal J.~S.~Levine,
% Comp.~Phys.~Comm.~\textbf{58} (1990) 181.
% \bibitem{axodraw} Jos Vermaseren, \texttt{axodraw}.
% \bibitem{mfpic} Thomas E.~Leathrum, \texttt{mfpic}.
% \bibitem{madgraph} Tim Stelzer and Bill Long, \texttt{MADGRAPH},
% hep-ph/93mmxxx.
% \end{thebibliography}
%
% \PrintIndex
%
% \PrintChanges
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \appendix
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Driver file}
%
% \begin{macrocode}
%<*driver>
\documentclass{article}
\usepackage{doc}
% \end{macrocode}
% The \MF{} and \MP{} logos come out much nicer if you have |mflogo|
% installed:
% \begin{macrocode}
\IfFileExists{mflogo.sty}%
{\usepackage{mflogo}%
\def\FMF{\texttt{feyn}\textlogo{MF}}}%
{\def\MF{\textsf{META}\-\textsf{FONT}}%
\def\MP{\textsf{META}\-\textsf{POST}}%
\def\FMF{\texttt{feyn}\textsf{MF}}}
% \end{macrocode}
% Here is the place to declare your own PostScript aware |dvi| driver
% option:
% \begin{macrocode}
%\usepackage[dvips]{feynmp}
%\usepackage{feynmf}
\font\manfnt=manfnt
\def\dangerousbend/{{\manfnt\char"7F}}
\def\dubious{\begin{itemize}\item[\dangerousbend/]}
\def\enddubious{\end{itemize}}
\parindent0pt
\EnableCrossrefs
\RecordChanges
\CodelineIndex
\DoNotIndex{\def,\gdef,\long,\let,\begin,\end,\if,\ifx,\else,\fi}
\DoNotIndex{\immediate,\write,\newwrite,\openout,\closeout,\typeout}
\DoNotIndex{\font,\nullfont,\jobname,\documentclass}
\DoNotIndex{\batchmode,\errorstopmode,\char,\catcode,\ }
\DoNotIndex{\CodelineIndex,\docdate,\DocInput,\DoNotIndex,\EnableCrossrefs}
\DoNotIndex{\filedate,\filename,\fileversion,\logo,\manfnt}
\DoNotIndex{\NeedsTeXFormat,\ProvidesPackage,\RecordChanges,\space}
\DoNotIndex{\usepackage,\wlog,\@gobble,\@ifundefined,\@namedef,\@spaces}
\DoNotIndex{\begingroup,\csname,\edef,\endcsname,\expandafter,\hbox}
\DoNotIndex{\hskip,\ifeof,\ignorespaces,\item,\leavevmode,\loop,\makebox}
\DoNotIndex{\newcounter,\newif,\newread,\openin,\par,\parindent,\put}
\DoNotIndex{\read,\relax,\repeat,\setcounter,\stepcounter,\the}
\DoNotIndex{\value,\vbox,\vskip}
\DoNotIndex{}
\begin{document}
\DocInput{feynmf.dtx}
\end{document}
%
% \end{macrocode}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Copying}
% \label{sec:GPL}
%
% \FMF{} is free software; you can redistribute it and/or modify it
% under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2, or (at your option)
% any later version.
%
% \FMF{} is distributed in the hope that it will be useful, but
% \emph{without any warranty}; without even the implied warranty of
% \emph{merchantability} or \emph{fitness for a particular purpose}.
% See the GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\endinput
Local Variables:
mode:LaTeX
change-log-default-name:"TODO"
fill-prefix:"% "
page-delimiter:"^% %%%%%%%%%*\n"
End: