#LyX 2.4 created this file. For more info see https://www.lyx.org/
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\pdf_title "Feynman Diagrams"
\pdf_author "LyX Team, Uwe Stöhr, Ronen Abravanel"
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\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 create 
\noun on
Feynman
\noun default
 diagrams,
 the \SpecialChar LaTeX
-package 
\series bold
feyn
\series default
 must be installed.
 A 
\noun on
Feynman
\noun default
 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 booktabs="true" tabularvalignment="middle">
<column alignment="center" valignment="middle" width="28col%">
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<column alignment="center" valignment="middle" width="20col%">
<row>
<cell alignment="center" valignment="top" topline="true" usebox="none">
\begin_inset Text

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Commands
\end_layout

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</cell>
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\begin_inset Text

\begin_layout Plain Layout
Description
\end_layout

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</cell>
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\begin_inset Text

\begin_layout Plain Layout
Example
\end_layout

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\begin_inset Text

\begin_layout Plain Layout
Result
\end_layout

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</cell>
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f,g,h
\end_layout

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</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
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<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
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\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

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</cell>
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fu,fd,fv (gu,gd,gv)
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<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 tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="middle">
<row>
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\begin_inset Text

\begin_layout Plain Layout
fd
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<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
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</cell>
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\begin_layout Plain Layout

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fv
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\begin_inset Text

\begin_layout Plain Layout

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\end_inset


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

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fA,fV
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</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
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\begin_inset Text

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<features tabularvalignment="middle">
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fdA
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fuV
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\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
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\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
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\end_inset


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

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fl,glB,glS,fl1,gl2,
 etc.
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</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
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\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 tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="middle">
<row>
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\begin_inset Text

\begin_layout Plain Layout
f
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<cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
gl
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<cell alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

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

\begin_layout Plain Layout

\end_layout

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

\begin_layout Plain Layout
f
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\end_inset
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<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
f
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\end_inset


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</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 $\backslash\mathrm{momentum}\{fA\}\{\vec{p\}}$
\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
the vertex label 
\emph on
p
\emph default
 is either '^' or '_' for labeling above or below the 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 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 $\backslash\mathrm{vertexlabel}^{e^{+}}fA$
\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 $fglS\backslash\mathrm{vertexlabel}_{\gamma}$
\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^{\mathrm{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 features of thepackage 
\series bold
feyn
\series default
 whose user manual can be found in 
\begin_inset CommandInset citation
LatexCommand cite
key "Feyn"
literal "true"

\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 align environments (which are described in section 
\begin_inset Quotes eld
\end_inset

Align Environments
\begin_inset Quotes erd
\end_inset

 of \SpecialChar LyX
's Math manual).
\end_layout

\end_inset


\end_layout

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

\end_inset


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

\end_inset

 of the \SpecialChar LaTeX
 package 
\series bold
feyn
\end_layout

\end_body
\end_document
