#LyX 2.1 created this file. For more info see http://www.lyx.org/
\lyxformat 474
\begin_document
\begin_header
\textclass scrartcl
\begin_preamble
% DO NOT ALTER THIS PREAMBLE!!!
%
% This preamble is designed to ensure that the file prints
% out as advertised. If you mess with this preamble,
% parts of this document may not print out as expected.  If you
% have problems LaTeXing this file, please contact 
% the documentation team
% email: lyx-docs@lists.lyx.org

% if pdflatex is used
\usepackage{ifpdf}
\ifpdf

% set fonts for nicer pdf view
\IfFileExists{lmodern.sty}
 {\usepackage{lmodern}}{}

\fi % end if pdflatex is used

% used to have extra space in table cells
\@ifundefined{extrarowheight}
 {\usepackage{array}}{}
\setlength{\extrarowheight}{5pt}
\end_preamble
\use_default_options true
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding auto
\fontencoding global
\font_roman default
\font_sans default
\font_typewriter default
\font_math auto
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize 12
\spacing single
\use_hyperref true
\pdf_title "Feynman Diagrams"
\pdf_author "LyX Team, Uwe Stöhr, Ronen Abravanel"
\pdf_bookmarks false
\pdf_bookmarksnumbered false
\pdf_bookmarksopen false
\pdf_bookmarksopenlevel 1
\pdf_breaklinks false
\pdf_pdfborder true
\pdf_colorlinks false
\pdf_backref false
\pdf_pdfusetitle false
\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
\papersize default
\use_geometry false
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 0
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 0
\use_package mhchem 1
\use_package stackrel 0
\use_package stmaryrd 0
\use_package undertilde 0
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date true
\justification true
\use_refstyle 0
\notefontcolor #0000ff
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation skip
\defskip medskip
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header

\begin_body

\begin_layout Title
Feynman Diagrams
\end_layout

\begin_layout Standard
\begin_inset Note Note
status open

\begin_layout Plain Layout
authors: Uwe Stöhr and Ronen Abravanel
\end_layout

\end_inset


\end_layout

\begin_layout Standard
To be able to use 
\noun on
Feynman
\noun default
 diagrams, the LaTeX-package 
\series bold
feyn
\series default
 must be installed.
 A Feynman diagram is created by inserting the command 
\series bold

\backslash
Diagram
\series default
 in a formula.
 Then you are able to add new matrix columns and rows like a normal matrices.
 
\end_layout

\begin_layout Standard
As matrix entry, one can enter commands that act as 
\begin_inset Quotes eld
\end_inset

particles
\begin_inset Quotes erd
\end_inset

 or 
\begin_inset Quotes eld
\end_inset

propagators
\begin_inset Quotes erd
\end_inset

, for example:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="4">
<features rotate="0" booktabs="true" tabularvalignment="middle">
<column alignment="center" valignment="middle" width="28col%">
<column alignment="center" valignment="middle" width="20col%">
<column alignment="center" valignment="middle" width="25col%">
<column alignment="center" valignment="middle" width="20col%">
<row>
<cell alignment="center" valignment="top" topline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Commands
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Description
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Example
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Result
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
f,g,h
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\noindent
\align left
fermion, photon or ghost propagator.
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="1" columns="3">
<features rotate="0" tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
f
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
g
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
h
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Diagram{f & g & h}
$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
fu,fd,fv (gu,gd,gv)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\noindent
\align left
fermion/photon, going up/down/vertical
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="3">
<features rotate="0" tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="middle">
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
fd
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
gu
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
fv
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Diagram{fd &  & gu\\
 & fv
}
$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
fA,fV
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\noindent
\align left
A and V are modifiers to produce arrow going left/up or right/down
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="3">
<features rotate="0" tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="middle">
<row>
<cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
fdA
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
fuV
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
gvV
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Diagram{fdA &  & fuV\\
 & gvV
}
$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
fl,glB,glS,fl1,gl2, etc.
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\noindent
\align left
fermions/photons loop
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="3">
<features rotate="0" tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="middle">
<row>
<cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
f
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
gl
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
f
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
f
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Diagram{f & gl\\
 & f & f
}
$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
momentum{ch}{text}
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\noindent
\align left
particle-momentum specification
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\backslash{\rm momentum}\{fA\}\{\vec{p\}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Diagram{\momentum{fA}{\vec{p}}}
$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
vertexlabel{p}{text}
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\noindent
\align left
A vertex label 
\emph on
p
\emph default
 is ^ or _ for labeling above or below vertex
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="1">
<features rotate="0" tabularvalignment="middle">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\backslash{\rm vertexlabel}^{e^{+}}fA$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $fglS\backslash{\rm vertexlabel}_{\gamma}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Diagram{\vertexlabel^{{\rm e^{+}}}fA\\
fglS\vertexlabel_{\gamma}
}
$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
These are just some of the options in the 
\series bold
feyn
\series default
 package.
 Its user manual can be found in 
\begin_inset CommandInset citation
LatexCommand cite
key "Feyn"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Note:
\series default
 If you have an index list in your document and use one of the AMS theorem
 modules, you have to add the option 
\series bold
noglobalbang
\series default
 to the document class options in the document settings.
 This enables the usage of the '!' character in index entries (necessary
 for subentries) but might cause troubles with the AMS align and align*
 environments (which are described in section 
\begin_inset Quotes eld
\end_inset

Align Environments
\begin_inset Quotes erd
\end_inset

 of LyX's Math manual).
\end_layout

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "Feyn"

\end_inset


\begin_inset CommandInset href
LatexCommand href
name "Documentation"
target "http://mirror.ctan.org/fonts/feyn/feyn.pdf"

\end_inset

 of the LaTeX-Package 
\series bold
feyn
\end_layout

\end_body
\end_document