Manual updated.

includes.tex

@@ -515,6 +515,7 @@ \chapter{Loop integrals}
 \subfile{pages/FCLoopGraphPlot.tex}
 \subfile{pages/FCLoopIntegralToGraph.tex}
 \subfile{pages/FCLoopPropagatorsToLineMomenta.tex}
+\subfile{pages/FCLoopAddMissingHigherOrdersWarning.tex}
 \subfile{pages/FCLoopApplyTopologyMappings.tex}
 \subfile{pages/FCLoopCreateRuleGLIToGLI.tex}
 \subfile{pages/FCLoopFindMomentumShifts.tex}

pages/Development.tex

@@ -128,21 +128,17 @@ \subsection{Packages that use
 
 Starting with FeynCalc 9.0 one can easily write something like
 
-\begin{Shaded}
-\begin{Highlighting}[]
-\FunctionTok{BeginPackage}\OperatorTok{[}\StringTok{"MyPackage\textasciigrave{}"}\OperatorTok{,\{}\StringTok{"FeynCalc\textasciigrave{}"}\OperatorTok{\}]}
+``\texttt{mathematica BeginPackage[\allowbreak{}"MyPackage}``,\{''FeynCalc```\}{]}
 
-\NormalTok{MySP::usage}\ExtensionTok{=}
-\StringTok{"Description of MySP"}\NormalTok{;}
+MySP::usage= ``Description of MySP'';
 
-\FunctionTok{Begin}\OperatorTok{[}\StringTok{"\textasciigrave{}Private\textasciigrave{}"}\OperatorTok{]}\NormalTok{;}
+Begin{[}``\texttt{Private}''{]};
 
-\NormalTok{MySP}\OperatorTok{[}\AttributeTok{a\_}\OperatorTok{,}\AttributeTok{b\_}\OperatorTok{]}\ExtensionTok{:=}\NormalTok{ FCI}\OperatorTok{[}\NormalTok{SP}\OperatorTok{[}\FunctionTok{a}\OperatorTok{,}\FunctionTok{b}\OperatorTok{]]}\NormalTok{;}
+MySP{[}a\_,b\_{]}:= FCI{[}SP{[}a,b{]}{]};
 
-\FunctionTok{End}\OperatorTok{[]}
-\FunctionTok{EndPackage}\OperatorTok{[]}
-\end{Highlighting}
-\end{Shaded}
+End{[}{]} EndPackage{[}{]}
+
+```mathematica
 
 \hypertarget{package-or-add-on}{%
 \subsection{Package or add-on?}\label{package-or-add-on}}

pages/FCLoopAddMissingHigherOrdersWarning.tex

@@ -0,0 +1,72 @@
+% !TeX program = pdflatex
+% !TeX root = FCLoopAddMissingHigherOrdersWarning.tex
+
+\documentclass[../FeynCalcManual.tex]{subfiles}
+\begin{document}
+\hypertarget{fcloopaddmissinghigherorderswarning}{
+\section{FCLoopAddMissingHigherOrdersWarning}\label{fcloopaddmissinghigherorderswarning}\index{FCLoopAddMissingHigherOrdersWarning}}
+
+\texttt{FCLoopAddMissingHigherOrdersWarning[\allowbreak{}expr,\ \allowbreak{}ep,\ \allowbreak{}fun]}
+determines the highest \texttt{ep}-power \(n\) in the given expression
+and adds a warning flag of order \(\textrm{ep}^n+1\). This is meant to
+prevent incorrect results stemming insufficient high expansions of
+\texttt{expr} in \texttt{ep}
+
+\subsection{See also}
+
+\hyperlink{toc}{Overview},
+\hyperlink{fcfeynmanparametrize}{FCFeynmanParametrize},
+\hyperlink{fcfeynmanprepare}{FCFeynmanPrepare}.
+
+\subsection{Examples}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{FCLoopAddMissingHigherOrdersWarning}\OperatorTok{[}\DecValTok{1}\SpecialCharTok{/}\NormalTok{ep}\SpecialCharTok{\^{}}\DecValTok{2}\NormalTok{ cc1 }\SpecialCharTok{+} \DecValTok{1}\SpecialCharTok{/}\NormalTok{ep cc2}\OperatorTok{,}\NormalTok{ ep}\OperatorTok{,}\NormalTok{ epHelp}\OperatorTok{]}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{dmath*}\breakingcomma
+\frac{\text{cc1}}{\text{ep}^2}+\frac{\text{cc2}}{\text{ep}}+(1+i) \;\text{epHelp}
+\end{dmath*}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{FCLoopAddMissingHigherOrdersWarning}\OperatorTok{[}\NormalTok{cc1}\OperatorTok{,}\NormalTok{ ep}\OperatorTok{,}\NormalTok{ epHelp}\OperatorTok{]}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{dmath*}\breakingcomma
+\text{cc1}+(1+i) \;\text{ep} \;\text{epHelp}
+\end{dmath*}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{FCLoopAddMissingHigherOrdersWarning}\OperatorTok{[}\NormalTok{cc1}\OperatorTok{,}\NormalTok{ ep}\OperatorTok{,}\NormalTok{ epHelp}\OperatorTok{,} \FunctionTok{Complex} \OtherTok{{-}\textgreater{}} \ConstantTok{False}\OperatorTok{]}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{dmath*}\breakingcomma
+\text{cc1}+\text{ep} \;\text{epHelp}
+\end{dmath*}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{FCLoopAddMissingHigherOrdersWarning}\OperatorTok{[}\NormalTok{cc1}\OperatorTok{,}\NormalTok{ ep}\OperatorTok{,}\NormalTok{ epHelp}\OperatorTok{,} \FunctionTok{Names} \OtherTok{{-}\textgreater{}} \ConstantTok{False}\OperatorTok{]}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{dmath*}\breakingcomma
+\text{cc1}+(1+i) \;\text{ep} \;\text{epHelp}
+\end{dmath*}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{FCLoopAddMissingHigherOrdersWarning}\OperatorTok{[}\NormalTok{GLI}\OperatorTok{[}\NormalTok{topo1}\OperatorTok{,} \OperatorTok{\{}\DecValTok{1}\OperatorTok{,} \DecValTok{1}\OperatorTok{,} \DecValTok{1}\OperatorTok{,} \DecValTok{1}\OperatorTok{,} \DecValTok{1}\OperatorTok{\}]} \OtherTok{{-}\textgreater{}}\NormalTok{ cc1}\SpecialCharTok{/}\NormalTok{ep}\SpecialCharTok{\^{}}\DecValTok{2} \SpecialCharTok{+}\NormalTok{ cc2}\SpecialCharTok{/}\NormalTok{ep }\SpecialCharTok{+}\NormalTok{ cc3 }\OperatorTok{,}\NormalTok{ ep}\OperatorTok{,}\NormalTok{ epHelp}\OperatorTok{]}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{dmath*}\breakingcomma
+G^{\text{topo1}}(1,1,1,1,1)\to \frac{\text{cc1}}{\text{ep}^2}+\frac{\text{cc2}}{\text{ep}}+\text{cc3}+(1+i) \;\text{ep} \;\text{epHelp}(\text{topo1X11111})
+\end{dmath*}
+\end{document}

pages/FCLoopFromGLI.tex

@@ -22,14 +22,14 @@ \subsection{Examples}
 \begin{Shaded}
 \begin{Highlighting}[]
 \NormalTok{topos }\ExtensionTok{=} \OperatorTok{\{}
-\NormalTok{   FCTopology}\OperatorTok{[}\StringTok{"topoBox1L"}\OperatorTok{,} \OperatorTok{\{}\NormalTok{FAD}\OperatorTok{[\{}\FunctionTok{q}\OperatorTok{,}\NormalTok{ m0}\OperatorTok{\}],}\NormalTok{ FAD}\OperatorTok{[\{}\FunctionTok{q} \SpecialCharTok{+}\NormalTok{ p1}\OperatorTok{,}\NormalTok{ m1}\OperatorTok{\}],}\NormalTok{ FAD}\OperatorTok{[\{}\FunctionTok{q} \SpecialCharTok{+}\NormalTok{ p2}\OperatorTok{,}\NormalTok{ m2}\OperatorTok{\}],}\NormalTok{ FAD}\OperatorTok{[\{}\FunctionTok{q} \SpecialCharTok{+}\NormalTok{ p2}\OperatorTok{,}\NormalTok{ m3}\OperatorTok{\}]\},} 
+\NormalTok{   FCTopology}\OperatorTok{[}\StringTok{"topoBox1L"}\OperatorTok{,} \OperatorTok{\{}\NormalTok{FAD}\OperatorTok{[\{}\FunctionTok{q}\OperatorTok{,}\NormalTok{ m0}\OperatorTok{\}],}\NormalTok{ FAD}\OperatorTok{[\{}\FunctionTok{q} \SpecialCharTok{+}\NormalTok{ p1}\OperatorTok{,}\NormalTok{ m1}\OperatorTok{\}],}\NormalTok{ FAD}\OperatorTok{[\{}\FunctionTok{q} \SpecialCharTok{+}\NormalTok{ p2}\OperatorTok{,}\NormalTok{ m2}\OperatorTok{\}],}\NormalTok{ FAD}\OperatorTok{[\{}\FunctionTok{q} \SpecialCharTok{+}\NormalTok{ p3}\OperatorTok{,}\NormalTok{ m3}\OperatorTok{\}]\},} 
     \OperatorTok{\{}\FunctionTok{q}\OperatorTok{\},} \OperatorTok{\{}\NormalTok{p1}\OperatorTok{,}\NormalTok{ p2}\OperatorTok{,}\NormalTok{ p3}\OperatorTok{\},} \OperatorTok{\{\},} \OperatorTok{\{\}],} 
 \NormalTok{   FCTopology}\OperatorTok{[}\StringTok{"topoTad2L"}\OperatorTok{,} \OperatorTok{\{}\NormalTok{FAD}\OperatorTok{[\{}\NormalTok{q1}\OperatorTok{,}\NormalTok{ m1}\OperatorTok{\}],}\NormalTok{ FAD}\OperatorTok{[\{}\NormalTok{q2}\OperatorTok{,}\NormalTok{ m2}\OperatorTok{\}],}\NormalTok{ FAD}\OperatorTok{[\{}\NormalTok{q1 }\SpecialCharTok{{-}}\NormalTok{ q2}\OperatorTok{,} \DecValTok{0}\OperatorTok{\}]\},} \OperatorTok{\{}\NormalTok{q1}\OperatorTok{,}\NormalTok{ q2}\OperatorTok{\},} \OperatorTok{\{\},} \OperatorTok{\{\},} \OperatorTok{\{\}]\}}
 \end{Highlighting}
 \end{Shaded}
 
 \begin{dmath*}\breakingcomma
-\left\{\text{FCTopology}\left(\text{topoBox1L},\left\{\frac{1}{q^2-\text{m0}^2},\frac{1}{(\text{p1}+q)^2-\text{m1}^2},\frac{1}{(\text{p2}+q)^2-\text{m2}^2},\frac{1}{(\text{p2}+q)^2-\text{m3}^2}\right\},\{q\},\{\text{p1},\text{p2},\text{p3}\},\{\},\{\}\right),\text{FCTopology}\left(\text{topoTad2L},\left\{\frac{1}{\text{q1}^2-\text{m1}^2},\frac{1}{\text{q2}^2-\text{m2}^2},\frac{1}{(\text{q1}-\text{q2})^2}\right\},\{\text{q1},\text{q2}\},\{\},\{\},\{\}\right)\right\}
+\left\{\text{FCTopology}\left(\text{topoBox1L},\left\{\frac{1}{q^2-\text{m0}^2},\frac{1}{(\text{p1}+q)^2-\text{m1}^2},\frac{1}{(\text{p2}+q)^2-\text{m2}^2},\frac{1}{(\text{p3}+q)^2-\text{m3}^2}\right\},\{q\},\{\text{p1},\text{p2},\text{p3}\},\{\},\{\}\right),\text{FCTopology}\left(\text{topoTad2L},\left\{\frac{1}{\text{q1}^2-\text{m1}^2},\frac{1}{\text{q2}^2-\text{m2}^2},\frac{1}{(\text{q1}-\text{q2})^2}\right\},\{\text{q1},\text{q2}\},\{\},\{\},\{\}\right)\right\}
 \end{dmath*}
 
 \begin{Shaded}
@@ -49,7 +49,7 @@ \subsection{Examples}
 \end{Shaded}
 
 \begin{dmath*}\breakingcomma
-\frac{\text{a1}}{\left(q^2-\text{m0}^2\right) \left((\text{p1}+q)^2-\text{m1}^2\right) \left((\text{p2}+q)^2-\text{m2}^2\right) \left((\text{p2}+q)^2-\text{m3}^2\right)}+\frac{\text{a2}}{\left(\text{q1}^2-\text{m1}^2\right) \left(\text{q2}^2-\text{m2}^2\right)^2 (\text{q1}-\text{q2})^4}
+\frac{\text{a1}}{\left(q^2-\text{m0}^2\right) \left((\text{p1}+q)^2-\text{m1}^2\right) \left((\text{p2}+q)^2-\text{m2}^2\right) \left((\text{p3}+q)^2-\text{m3}^2\right)}+\frac{\text{a2}}{\left(\text{q1}^2-\text{m1}^2\right) \left(\text{q2}^2-\text{m2}^2\right)^2 (\text{q1}-\text{q2})^4}
 \end{dmath*}
 
 Notice that it is necessary to specify all topologies present in
@@ -65,7 +65,7 @@ \subsection{Examples}
 \FloatBarrier
 \begin{figure}[!ht]
 \centering
-\includegraphics[width=0.6\linewidth]{img/047duy8jklfe9.pdf}
+\includegraphics[width=0.6\linewidth]{img/0jtbiuq3nviq2.pdf}
 \end{figure}
 \FloatBarrier
 
@@ -85,7 +85,7 @@ \subsection{Examples}
 \end{Shaded}
 
 \begin{dmath*}\breakingcomma
-\frac{1}{\left(\text{FCGV}(\text{lmom21})^2-\text{m0}^2\right) \left((\text{p1}+\text{FCGV}(\text{lmom11}))^2-\text{m1}^2\right) \left((\text{p2}+\text{FCGV}(\text{lmom11}))^2-\text{m3}^2\right) \left((\text{p2}+\text{FCGV}(\text{lmom21}))^2-\text{m2}^2\right)}
+\frac{1}{\left(\text{FCGV}(\text{lmom21})^2-\text{m0}^2\right) \left((\text{p1}+\text{FCGV}(\text{lmom11}))^2-\text{m1}^2\right) \left((\text{p3}+\text{FCGV}(\text{lmom11}))^2-\text{m3}^2\right) \left((\text{p2}+\text{FCGV}(\text{lmom21}))^2-\text{m2}^2\right)}
 \end{dmath*}
 
 You can customize the naming scheme for the momenta via the
@@ -111,7 +111,7 @@ \subsection{Examples}
 \end{Shaded}
 
 \begin{dmath*}\breakingcomma
-\frac{1}{\left(\text{p22}^2-\text{m0}^2\right) \left((\text{p11}+\text{p1})^2-\text{m1}^2\right) \left((\text{p22}+\text{p2})^2-\text{m2}^2\right) \left((\text{p11}+\text{p2})^2-\text{m3}^2\right)}
+\frac{1}{\left(\text{p22}^2-\text{m0}^2\right) \left((\text{p11}+\text{p1})^2-\text{m1}^2\right) \left((\text{p22}+\text{p2})^2-\text{m2}^2\right) \left((\text{p11}+\text{p3})^2-\text{m3}^2\right)}
 \end{dmath*}
 
 In general, \texttt{FCLoopFromGLI} can change the ordering of
@@ -128,6 +128,6 @@ \subsection{Examples}
 \end{Shaded}
 
 \begin{dmath*}\breakingcomma
-\frac{\text{a1}}{\left(q^2-\text{m0}^2\right).\left((\text{p1}+q)^2-\text{m1}^2\right).\left((\text{p2}+q)^2-\text{m2}^2\right).\left((\text{p2}+q)^2-\text{m3}^2\right)}+\frac{\text{a2}}{\left(\text{q1}^2-\text{m1}^2\right).\left(\text{q2}^2-\text{m2}^2\right)^2.(\text{q1}-\text{q2})^4}
+\frac{\text{a1}}{\left(q^2-\text{m0}^2\right).\left((\text{p1}+q)^2-\text{m1}^2\right).\left((\text{p2}+q)^2-\text{m2}^2\right).\left((\text{p3}+q)^2-\text{m3}^2\right)}+\frac{\text{a2}}{\left(\text{q1}^2-\text{m1}^2\right).\left(\text{q2}^2-\text{m2}^2\right)^2.(\text{q1}-\text{q2})^4}
 \end{dmath*}
 \end{document}

pages/FeynCalc.tex

@@ -1040,6 +1040,9 @@ \section{Loop integrals}\label{loop integrals}\index{Loop integrals}}
   \hyperlink{../fcloopintegraltograph}{../FCLoopIntegralToGraph},
   \hyperlink{../fclooppropagatorstolinemomenta}{../FCLoopPropagatorsToLineMomenta}
   - create and plot graphs representing loop integrals
+\item
+  \hyperlink{../fcloopaddmissinghigherorderswarning}{../FCLoopAddMissingHigherOrdersWarning}
+  - adds a warning flag to the given \(\epsilon\)-expansion
 \item
   \hyperlink{../fcloopapplytopologymappings}{../FCLoopApplyTopologyMappings},
   \hyperlink{../fcloopcreateruleglitogli}{../FCLoopCreateRuleGLIToGLI},

pages/SFAD.tex

@@ -7,10 +7,10 @@
 \section{SFAD}\label{sfad}\index{SFAD}}
 
 \texttt{SFAD[\allowbreak{}\{\allowbreak{}\{\allowbreak{}q1 +...,\ \allowbreak{}p1 . q2 +...,\ \allowbreak{}\} \{\allowbreak{}m^2,\ \allowbreak{}s\},\ \allowbreak{}n\},\ \allowbreak{}...]}
-denotes a Cartesian propagator given by
+denotes a standard Lorentzian propagator given by
 \(\frac{1}{[(q_1+\ldots)^2 + p_1 \cdot q_2 ... + m^2 + s i \eta]^n}\),
-where \(q_1^2\) and \(p_1 \cdot q_2\) are Cartesian scalar products in
-\(D-1\) dimensions.
+where \(q_1^2\) and \(p_1 \cdot q_2\) are Lorentzian scalar products in
+\(D\) dimensions.
 
 For brevity one can also use shorter forms such as
 \texttt{SFAD[\allowbreak{}\{\allowbreak{}q1+ ...,\ \allowbreak{} m^2\},\ \allowbreak{}...]},
@@ -19,12 +19,18 @@ \section{SFAD}\label{sfad}\index{SFAD}}
 \texttt{SFAD[\allowbreak{}q1,\ \allowbreak{}...]} etc.
 
 If \texttt{s} is not explicitly specified, its value is determined by
-the option \texttt{EtaSign}, which has the default value \texttt{+1}.
+the option \texttt{EtaSign}, which has the default value \texttt{+1} and
+corresponds to \(+ i \eta\)
 
 If \texttt{n} is not explicitly specified, then the default value
-\texttt{1} is assumed. Translation into FeynCalcI internal form is
-performed by \texttt{FeynCalcInternal}, where a \texttt{SFAD} is encoded
-using the special head \texttt{CartesianPropagatorDenominator}.
+\texttt{1} is assumed. Translation into the FeynCalc internal form is
+performed by \texttt{FeynCalcInternal}, where an \texttt{SFAD} is
+encoded using the special head \texttt{StandardPropagatorDenominator}.
+
+\texttt{SFAD} can represent more versatile propagators as compared to
+the old \texttt{FAD}. In particular, \texttt{FAD} does not allow one to
+enter eikonal propagators, track the sign of the \(i \eta\) or change
+the sign and the form of the mass term.
 
 \subsection{See also}
 
@@ -82,4 +88,60 @@ \subsection{Examples}
 \begin{dmath*}\breakingcomma
 \frac{1}{(n\cdot q+i \eta )}
 \end{dmath*}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{SFAD}\OperatorTok{[\{\{}\FunctionTok{p}\OperatorTok{,} \FunctionTok{p}\NormalTok{ . }\FunctionTok{q}\OperatorTok{\},} \FunctionTok{m}\SpecialCharTok{\^{}}\DecValTok{2}\OperatorTok{\}]}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{dmath*}\breakingcomma
+\frac{1}{(p^2+p\cdot q-m^2+i \eta )}
+\end{dmath*}
+
+The so called Smirnov-notation for propagators can be achieved by
+multiplying the quadratic part by \texttt{I} and switching the sign of
+the mass term.
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{SFAD}\OperatorTok{[\{\{}\FunctionTok{I}\SpecialCharTok{*}\FunctionTok{p}\OperatorTok{,} \DecValTok{0}\OperatorTok{\},} \SpecialCharTok{{-}}\FunctionTok{m}\SpecialCharTok{\^{}}\DecValTok{2}\OperatorTok{\}]}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{dmath*}\breakingcomma
+\frac{1}{(-p^2+m^2+i \eta )}
+\end{dmath*}
+
+If one wants to have additional variables multiplying loop or external
+momenta, those need to be declared to be of the \texttt{FCVariable} type
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{DataType}\OperatorTok{[}\NormalTok{la}\OperatorTok{,}\NormalTok{ FCVariable}\OperatorTok{]} \ExtensionTok{=} \ConstantTok{True}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{dmath*}\breakingcomma
+\text{True}
+\end{dmath*}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{SFAD}\OperatorTok{[\{\{}\DecValTok{0}\OperatorTok{,}\NormalTok{ la }\FunctionTok{p}\NormalTok{ . }\FunctionTok{q}\OperatorTok{\},} \FunctionTok{m}\SpecialCharTok{\^{}}\DecValTok{2}\OperatorTok{\}]}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{dmath*}\breakingcomma
+\frac{1}{(\text{la} (p\cdot q)-m^2+i \eta )}
+\end{dmath*}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\SpecialCharTok{\%} \SpecialCharTok{//}\NormalTok{ FCI }\SpecialCharTok{//} \FunctionTok{StandardForm}
+
+\CommentTok{(*FeynAmpDenominator[StandardPropagatorDenominator[0, la Pair[Momentum[p, D], Momentum[q, D]], {-}m\^{}2, \{1, 1\}]]*)}
+\end{Highlighting}
+\end{Shaded}
+
 \end{document}