% \iffalse % This is feyn.dtx, which manages the use of the feyn Metafont % %% This software is copyright, 1991, 1994, 2001, 2002, 2005, 2008, 2009 Norman Gray. %% %% This program 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 %% of the License, or (at your option) any later version. %% %% This program 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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. %% %% Author: Norman Gray, norman@astro.gla.ac.uk. %% Department of Physics and Astronomy, University of Glasgow, UK %% %% See the file LICENCE for a copy of the GPL. %% You can also find an online copy at http://www.gnu.org/copyleft/gpl.html . % %<+package|driver>%% VCS Info: Mercurial revision 204fc9a2e560, 2009-10-08 12:56 +0100 %<+package>\NeedsTeXFormat{LaTeX2e} %<+package>\ProvidesPackage{feyn}[2009/10/08 \space0.3.3\space textpos] %<+package>\typeout{Package: `feyn' 0.3.3\space<2009/10/08 >} % %<*driver> \documentclass{ltxdoc} \usepackage{feyn} \title{The feyn font} \author{Norman Gray\\(\texttt{norman@astro.gla.ac.uk})} \date{Version 0.3.3, 2009 October 8} \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} % % % \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 \~} % % % % % % % \newcommand{\pslash}{p\llap{/\kern-0.3pt}} % \newcommand{\feynx}{\textsl{feyn}} % \newcommand{\metafont}{Metafont} % % % This describes the font \feynx, which can be used to produce relatively % simple Feynman diagrams within equations in a \LaTeX\ document. % % 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 write simple diagrams, within equations or within text, % in a size matching the surrounding text size. % % \iffalse % \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 which % seem to appear most often in non-figure displays (the practical % definition of `appear most often' 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.. % % % \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 & 1 & 0 \cr \tableskip % flS & flS & fermion loop (small)$^{\dag\ddag}$ % & 0 & 1 & 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 % & 2 & 0 & 0 \cr \tableskip % hs & hs & short ghost % & 1 & 0 & 0 \cr \tableskip % hu & hu & upward ghost (45$^\circ$) % & $\sqrt2$ & $\sqrt2$ & 0 \cr \tableskip % hd & hd & downward ghost % & $\sqrt2$ & $\sqrt2$ & 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 & 0 & 0 & 0 \cr % } % \caption{\label{chars} The characters in font \feynx. 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'.} % \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. % % The unnassigned positions in the \feynx\ font are filled % with an obviously wrong dummy character, so that |$\feyn{A}$|, for example, % produces $\feyn{fs0Afs0}$. % % 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'. See below for % examples. This is rarely used as such, since the |\feyn| and |\Feyn| % commands make~`!' a temporarily active character, and define it % to be |\momentum|. % \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|. % \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. % % \section{Examples} % % \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}} % % 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} % $\end{examplerhs} % \end{codeexample} % % The |\Diagram| command lays out its arguments as an array. % \begin{codeexample} % \begin{verbatim} % \Diagram{\vertexlabel^a \\ % fd \\ % & g\vertexlabel_{\mu,c} \\ % \vertexlabel_b fu\\ % } % = \displaystyle % ig\gamma_\mu (T^c)_{ab} % \end{verbatim} % \Becomes % \begin{examplerhs}$ % \Diagram{\vertexlabel^a \\ % fd \\ % & g\vertexlabel_{\mu,c} \\ % \vertexlabel_b fu\\ % } % = \displaystyle % 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''. % % \begin{codeexample} % \begin{verbatim} % \feyn{ms mA gl gv ms x f} % \end{verbatim} % \Becomes % $\feyn{ms mA gl gv ms x f}$ % \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} % {\newline % \vbox{\hrule\hbox to \textwidth{\vrule height 1.5ex\hfil\vrule}}% % \parskip0pt} % {\vbox{\hbox to \textwidth{\vrule height 1.5ex \hfil\vrule}\hrule}} % % Bremsstrahlung: % \begin{bigdisplay} % \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} % % 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''. % % The expression for the heavy-fermion self-energy in the \textsc{ope} is: % \begin{bigdisplay} % \begin{verbatim} % \def\bracket#1{\langle #1 \rangle} % \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[ \Diagram{ &x &x \\ % &gv &gv \\ % fs &fs &fs \\} + \cdots \right] % \bracket{G_{\mu\nu}^a G_{\mu\nu}^a}\\ % \end{eqnarray*} % \end{verbatim} % \hrule % \def\bracket#1{\langle #1 \rangle} % \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[ \Diagram{ &x &x \\ % &gv &gv \\ % fs &fs &fs \\} + \cdots \right] % \bracket{G_{\mu\nu}^a G_{\mu\nu}^a}\\ % \end{eqnarray*} % \end{bigdisplay} % % The Feynman Rules are as follows: % \begin{bigdisplay} % \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} % \hrule % \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} % % The diagrams can also appear as parts of equations: % \begin{bigdisplay} % \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} % % You should be able to find generic instructions for installing % \LaTeX\ files at % \url{http://www.tex.ac.uk/cgi-bin/texfaq2html?label=installthings}. % % 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 or teTeX (which is true of most Unix % installations, and most MacOS\,X 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}. % % Users of other systems will have similar mechanisms % for finding and confirming the search paths (and if anyone wishes to % send me details, I can add the details to this document). % % \subsection*{Acknowledgements} % % Thanks to Purnendu Chakraborty, Fabio Correa, and Bryan Chen for % suggestions and testing 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} % % 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} % \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@} \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@}} \fi \def\feyn@#1{\feyn@alphabet{#1}\endgroup} \def\Feyn@#1{\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 |"7F| in the feyn font is blank, but has 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}{"7F} \setbox0=\hbox{$\FeynSpaceChar$} \newdimen\feyn@mfmodule \feyn@mfmodule=\wd0 \newdimen\feyn@module \feyn@module=2\wd0 \newdimen\feyn@maxis \feyn@maxis=\ht0 % \end{macrocode} % \end{macro} % \end{macro} % % \begin{macro}{\Diagram} % Define the |\Diagram| macro, which lays out a semi-complicated % diagram in 2-d. % \begin{macrocode} {\catcode`\!=\active \gdef\Diagram{% \begingroup % ends in \Diagram@ \catcode`\!=\active \let!\momentum \Diagram@}} \def\Diagram@#1{\setbox0=\hbox{\vbox{\offinterlineskip \let\\\cr \halign{&$\displaystyle\feyn{##}$\cr #1\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 \vcenter{\box0}% \endgroup}% end group begun in \Diagram % \end{macrocode} % \end{macro} % % \begin{macro}{\maxis} % Raise the argument to the math axis. % \begin{macrocode} \def\maxis#1{\raise\feyn@maxis \hbox{$#1$}} % \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@mfmodule \divide\feyn@nudge by 3 % \end{macrocode} % % The various |\feyn@pos@| 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@| macros. The % || 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}% "f" \feyn@annotation{fA}{0.99974}{0.35}{top}% "F" \feyn@annotation{fV}{0.99974}{0.35}{top}% 6 \feyn@annotation{fu}{0.70692}{0.95692}{ulft}% "e" \feyn@annotation{fuA}{0.70692}{0.95692}{ulft}% "E" \feyn@annotation{fuV}{0.70692}{0.95692}{ulft}% 5 \feyn@annotation{fd}{0.70692}{0.95692}{urt}% "d" \feyn@annotation{fdA}{0.70692}{0.95692}{urt}% "D" \feyn@annotation{fdV}{0.70692}{0.95692}{urt}% 4 \feyn@annotation{fv}{0}{1.24974}{urt}% "b" \feyn@annotation{fvA}{0}{1.24974}{urt}% "B" \feyn@annotation{fvV}{0}{1.24974}{urt}% 2 \feyn@annotation{m}{0.99974}{0.32802}{top}% "m" \feyn@annotation{mA}{0.99974}{0.32802}{top}% "M" \feyn@annotation{mV}{0.99974}{0.32802}{top}% 13 \feyn@annotation{ms}{0.49986}{0.32802}{top}% 11 \feyn@annotation{fl}{0}{1.85}{top}% "l" \feyn@annotation{flA}{0}{1.85}{top}% "L" \feyn@annotation{flV}{0}{1.85}{top}% 12 \feyn@annotation{flu}{0}{-1.35}{bot}% "n" \feyn@annotation{fluA}{0}{-1.35}{bot}% "N" \feyn@annotation{fluV}{0}{-1.35}{bot}% 14 \feyn@annotation{flS}{0}{1.23335}{top}% "o" \feyn@annotation{flSA}{0}{1.23335}{top}% "O" \feyn@annotation{flSV}{0}{1.23335}{top}% 15 \feyn@annotation{flSu}{0}{-0.90001}{bot}% "w" \feyn@annotation{flSuA}{0}{-0.90001}{bot}% "W" \feyn@annotation{flSuV}{0}{-0.90001}{bot}% 23 \feyn@annotation{g}{0.99974}{0.45}{top}% "g" \feyn@annotation{gA}{0.99974}{0.45}{top}% "G" \feyn@annotation{gV}{0.99974}{0.45}{top}% 7 \feyn@annotation{gu}{0.70692}{0.95692}{ulft}% "u" \feyn@annotation{guA}{0.70692}{0.95692}{ulft}% "U" \feyn@annotation{guV}{0.70692}{0.95692}{ulft}% 21 \feyn@annotation{gd}{0.70692}{0.95692}{urt}% "v" \feyn@annotation{gdA}{0.70692}{0.95692}{urt}% "V" \feyn@annotation{gdV}{0.70692}{0.95692}{urt}% 22 \feyn@annotation{gv}{0}{1.24974}{urt}% "}" \feyn@annotation{gvA}{0}{1.24974}{urt}% "]" \feyn@annotation{gvV}{0}{1.24974}{urt}% 29 \feyn@annotation{g1}{-1.41422}{1.66422}{ulft}% "q" \feyn@annotation{g1A}{-1.41422}{1.66422}{ulft}% "Q" \feyn@annotation{g1V}{-1.41422}{1.66422}{ulft}% 17 \feyn@annotation{g2}{1.41422}{1.66422}{urt}% "r" \feyn@annotation{g2A}{1.41422}{1.66422}{urt}% "R" \feyn@annotation{g2V}{1.41422}{1.66422}{urt}% 18 \feyn@annotation{g3}{1.41422}{-1.16422}{lrt}% "s" \feyn@annotation{g3A}{1.41422}{-1.16422}{lrt}% "S" \feyn@annotation{g3V}{1.41422}{-1.16422}{lrt}% 19 \feyn@annotation{g4}{-1.41422}{-1.16422}{llft}% "t" \feyn@annotation{g4A}{-1.41422}{-1.16422}{llft}% "T" \feyn@annotation{g4V}{-1.41422}{-1.16422}{llft}% 20 \feyn@annotation{gl}{0}{2.25}{urt}% "y" \feyn@annotation{glA}{0}{2.25}{urt}% "Y" \feyn@annotation{glV}{0}{2.25}{urt}% 25 \feyn@annotation{glu}{0}{-1.75}{llft}% "z" \feyn@annotation{gluA}{0}{-1.75}{llft}% "Z" \feyn@annotation{gluV}{0}{-1.75}{llft}% 26 \feyn@annotation{glB}{0}{2.91667}{urt}% "{" \feyn@annotation{glBA}{0}{2.91667}{urt}% "[" \feyn@annotation{glBV}{0}{2.91667}{urt}% 27 \feyn@annotation{glS}{0}{1.5833}{llft}% "|" \feyn@annotation{glSA}{0}{1.5833}{llft}% "\" \feyn@annotation{glSV}{0}{1.5833}{llft}% 28 \feyn@annotation{h}{0.99974}{0.25}{top}% "h" \feyn@annotation{hA}{0.99974}{0.25}{top}% "H" \feyn@annotation{hV}{0.99974}{0.25}{top}% 8 \feyn@annotation{hu}{0.70464}{0.95464}{ulft}% "i" \feyn@annotation{huA}{0.70464}{0.95464}{ulft}% "I" \feyn@annotation{huV}{0.70464}{0.95464}{ulft}% 9 \feyn@annotation{hd}{0.70464}{0.95464}{urt}% "j" \feyn@annotation{hdA}{0.70464}{0.95464}{urt}% "J" \feyn@annotation{hdV}{0.70464}{0.95464}{urt}% 10 \feyn@annotation{hs}{0.49986}{0.25}{top}% "K" \feyn@annotation{c}{0.65044}{0.90044}{top}% "c" \feyn@annotation{p}{0.65}{0.9}{top}% "p" \feyn@annotation{P}{0.65044}{0.90044}{top}% "P" \feyn@annotation{x}{0}{0.55641}{top}% "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