%---------------------------------------------------------------------------
%
% About FeynCalc
%
% --------------------------------------------------------------------------
\documentclass{article}
\newcommand{\mma}{{\it Mathematica}}
\begin{document}
{\bf \large FeynCalc 3.1 -- Tools for Elementary Particle Physics}
~\\~
\begin{center}
Rolf Mertig \\
Mertig Research \& Consulting \\
http://www.mertig.com
\end{center}
~\\~
\noindent
FeynCalc 3.1 is a \mma\ \cite{mathematica}
package for algebraic calculations in elementary particle physics.
Calculational and database tools are provided for frequently occuring tasks.
Some of those are:
\begin{itemize}
\item Lorentz index contraction and Dirac algebra manipulation ({\tt Contract, Calc})
\item color factor calculation and simplification for SU(N) ({\tt SUNSimplify})
\item automatic Feynman rule derivation ({\tt FeynRule})
\item automatic 1-loop diagram simplification up to box graphs {(\tt OneLoopSimplify},
{\tt OneLoop}, {\tt OneLoopSum})
\item general noncommutative algebra and special noncommutative operator algebra
({\tt DotSimplify, ExpandPartialD})
\item look-up tables for Feynman parameter and moment integrals ({\tt Integrate2}),
convolutions ({\tt Convolute}) and Feynman rules ({\tt Twist2GluonOperator})
\item special translation facilities to change FeynCalc
syntax to and from FORM \cite{Vermaseren} syntax ({\tt FeynCalc2FORM, FORM2FeynCalc})
\item optimized Fortran generation with {\tt Isolate} and {\tt Write2}.
\end{itemize}
Many more useful functions like, e.g., {\tt SimplifyPolyLog} for simplification of polylogs and logs
of real arguments, {\tt Series2} for optimized Taylor expansion of Gamma functions, are
implemented in FeynCalc in a modular and extendable way.
FeynCalc 3.1 is partially based on an earlier FeynCalc version \cite{Mertig:1990an} and on algorithms
described in \cite{Denner:1993kt}.
Since FeynCalc is completely programmed in the \mma\ language, a speed
penalty is unavoidable. Thus, the 4-loop QCD $\beta$-function can and should be
only calculated with FORM, but the author and others have calculated without any problem
2-loop QCD and Standard Model self-energies in FeynCalc, and with sufficient effort and CPU-time
also 3-loop self-energies should be possible.
However, FeynCalc is much more convenient to use for simple and medium sized
calculations than FORM, just because FeynCalc uses a functional programming paradigm,
while FORM is procedure-based and the expert user has to do a lot of programming.
As a further benefit the FeynCalc user has all the other facilities
of \mma\, like typesetting, graphics, etc., at hand. Also it is rather easy to automatically
write and call existent FORM programs from within FeynCalc. This hybrid approach of using the
best of both worlds has been used successfully for the original calculation of the
2-loop spin splitting functions \cite{Mertig:1996ny}.
Further applications of FeynCalc were the 1-loop radiative corrections to
$e^+ e^- \to H Z$, high energy approximation of $e^+ e^- \to W^+ W^-$,
$gg \to t \bar{t}$, and many more (see http://www.feyncalc.com for a link to a complete list).
FeynCalc was not able, due to the speed problem of \mma, to perform
a full 1-loop calculation of $W^+ W^- \to W^+ W^-$, which has been done in
\cite{Denner:1997kq} using LoopTools \cite{Hahn:1998yk}.
Compared to LoopTools, which is based on FORM, FeynCalc is much slower
but offers more functionality, e.g., to algebraically reduce Passarino-Veltman
integrals to scalar integrals.
FeynCalc 3.1 is still compatible with FeynArts 2.2
(for updated versions see http://www-itp.physik.uni-karlsruhe.de/feynarts)
if the FeynArts function {\tt ToFA1Convention} is used on the generated amplitudes.
TARCER \cite{Mertig:1998vk} is a FeynCalc-compatible free program to calculate
massive 2-loop propagator-type moment integrals.
The latest commercial version FeynCalc 3.1 is an add-on to \mma\ 3.0.
The manual has a lot of examples and is freely available, e.g.,
from http://www.feyncalc.com.
The user base of FeynCalc consists of theoretical physicists around the world
working in QCD, the Standard Model and minimal extensions,
chiral perturbation theory and similar theories.
FeynCalc can also be used in Quantum Field Theory courses, since it enables the students
to perform more difficult calculations in seconds or minutes, and thus get less
%annoyed by the sometimes quite exhausting technical complications of contemporary
theoretical physics.
{\small
\begin{thebibliography}{1}
\bibitem{Denner:1993kt}
A.~Denner.
\newblock {Techniques for calculation of electroweak radiative corrections at
the one loop level and results for W physics at LEP200}.
\newblock {\em Fortschr. Phys.}, 41:307--420, 1993.
\bibitem{Vermaseren}
J.A.M Vermaseren, {\it Symbolic Manipulation with FORM},
(Computer Algebra Netherlands, Amsterdam, 1991).
\bibitem{Denner:1997kq}
A.~Denner and T.~Hahn.
\newblock {Radiative corrections to $W^+ W^- \to W^+ W^-$ in the electroweak
standard model}.
\newblock {\em Nucl. Phys.}, B525:27, 1998.
\bibitem{Hahn:1998yk}
T.~Hahn and M.~Perez-Victoria.
\newblock {Automatized one loop calculations in four-dimensions and D-
dimensions}.
\newblock 1998.
\bibitem{mathematica}
Stephen Wolfram, {\it The Mathematica Book}, 3rd ed.
\newblock{Wolfram Media /Cambridge University Press, 1996}.
\bibitem{Mertig:1990an}
R.~Mertig, M.~B{\"o}hm, and A.~Denner.
\newblock {FeynCalc: Computer algebraic calculation of Feynman amplitudes}.
\newblock {\em Comput. Phys. Commun.}, 64:345, 1991.
\bibitem{Mertig:1998vk}
R.~Mertig and R.~Scharf.
\newblock {TARCER: A Mathematica program for the reduction of two loop
propagator integrals}.
\newblock {\em Comput. Phys. Commun.}, 111:265, 1998.
\bibitem{Mertig:1996ny}
R.~Mertig and W.~L. van Neerven.
\newblock {The Calculation of the Two-Loop Spin Splitting Functions
$P_{ij}^{(1)}(x)$}.
\newblock {\em Z. Phys.}, C70:637--654, 1996.
\end{thebibliography}
}
\end{document}