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" in High Energy Physics: \nFeynCalc 3.0"
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Cell["\<\
A theoretical physicist uses a Mathematica 3.0 program and database \
for assistance in Feynman diagram calculations.\
\>", "Subsubtitle"],
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Cell["by Rolf Mertig", "Subtitle"],
Cell["\<\
Three of the four fundamental forces of nature are described by the \
so-called \"Standard Model\", which can make quantitative predictions once a \
small number of free parameters are fitted to experiments. At present, the \
experimental verification (non-falsification) of this Standard Model of the \
electromagnetic, weak and strong interactions has changed from a qualitative \
level to a quantitative one, where the comparison of the numbers produced by \
experiment and the numbers predicted from the theoretical framework becomes \
very involved, both from the experimental and from the theoretical side. \
\
\>", "Text"],
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"In order to evaluate the theory at a more precise quantitative level, \
so-called ",
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" ",
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" have to be calculated. Feynman diagrams (invented by Nobel laureate \
Richard Feynman) are simple pictures describing the\[LongDash]in fact, not so \
simple\[LongDash]interactions of elementary particles. These diagrams are \
translated into complicated mathematical expressions and have to be evaluated \
by an algorithm, which even Feynman himself thought of feeding into a \
computer."
}], "Text"],
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"FeynCalc was written to automate the calculation of Feynman diagrams. The \
first version of FeynCalc was used to calculate a number of 1-loop 2\
\[LongRightArrow] 2 processes. Apart from performing complicated \
loop-calculations (higher order perturbative contributions to the Born-level \
approximation), FeynCalc was designed and used as an easy interactive tool to \
do non-indicial tensor algebra; for example, contracting Lorentz indices, \
performing Dirac traces, simplifying SU(3) color-algebra expressions, and \
incorporating other special functions and features from theoretical physics \
into the powerful general ",
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" environment. Especially in theoretical calculations involving non-zero \
masses of the elementary particles. ",
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"'s capabilities of factorization of large expressions proved very useful \
in obtaining a short result. With the advent of ",
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" 3.0 (the alpha- and beta- versions, which the author had the privilege of \
testing over the last three years), the reorganisation of the algebraical \
engine proved extremely useful in the solution of several hard problems in \
2-loop QCD calculations."
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"As a true theoretical physicist, I never thought that a user interface \
like the ",
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" Front End would be of any use, and thus I only started to play with it \
when the first alpha-version with typesetting arrived on a NeXTstation of the \
department. Quite soon I changed my mind, since the new automatic typesetting \
capabilities (especially the automatic real-time linebreaking!) of the new ",
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" proved extremely useful in several aspects. First of all, I could display \
and print out intermediate results in a human-readable form, so that my \
collaborator (a ",
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" illiterate) could also read it. Secondly, and certainly more important, I \
found programming mistakes in larger formulas much more easily, since a \
nicely two-dimensional typeset output is easier to read and more information \
fits on a given screen (or paper) surface. Of course the programmability of \
the typesetting was a very nice feature too, so that a dirac matrix ",
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Cell["The origin of FeynCalc", "Subsection"],
Cell["\<\
The roots of FeynCalc go back to 1987. During a stay as a graduate \
student in Albuquerque, New Mexico, I learned to program in Macsyma from the \
experts Stanly Steinberg and Michael Wester. Meanwhile in Germany, elementary \
particle physicists needed someone to automate the calculation of Feynman \
diagrams. The algorithms were provided mostly by Ansgar Denner and Manfred B\
\[ODoubleDot]hm and implemented in a purely functional way by me during the \
years 1987 - 1989. \
\>", "Text"],
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"The basic idea was to have general functions for some of the more mechanical \
parts of the diagram calculations\[LongDash]highly generalizable tools for \
use in calculations of different physical (1-loop) processes, especially 1\
\[Rule]2 and 2\[Rule]2 processes. These included tools for"], "Text"],
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"\[Bullet] Lorentz algebra : \n ",
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"Applications",
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"of these tools included complete 1-loop processes in the Standard Model: \n\
\n \t\t ",
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Cell["\<\
However, at the end of 1989 several problems showed up with the \
Macsyma implementation. The purely functional programming style proved to be \
difficult to debug and, in fact, inappropriate. The rudimentary pattern \
matcher in Macsyma was not useful. There was no way to incorporate new \
functions easily into the whole Macsyma system, and no possibility of \
providing online documentation. Furthermore, Macsyma's memory managment \
(\"garbage collection\") was slow when handling large expressions.\
\>",
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"\n "
}], "Subsubsection"],
Cell["\<\
In 1990, user-friendly packages were built with extended automatic \
capabilites (OneLoop, OneLoopSum), and SU(3) algebra capabilities were added \
(SU3Simplify).\
\>", "Text"],
Cell["\<\
In 1991 I began to write documentation and make the program \
available on anonymous ftp-servers: mathsource.wolfram.com and \
canc.can.nl\
\>", "Text"],
Cell[TextData[{
"Applications from 1990 - 1996 included:\n\n\[Bullet]1-loop 2 \[Rule]2 \
processes in the Standard Model, such as:\n ",
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1992-1995 : FeynCalc 2.0-2.2, unification and simplification.\
\>",
"Subsubsection"],
Cell[TextData[{
"During this period of development the SU(3) algebra was changed to SU(N). \
Several tools for automatic tree-level calculation were added, for example \
the function ",
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". (Unfortunately, the documentation was not updated.) All sub-packages \
were put into one file ",
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" lines). The result was FeynCalc2.2beta.m, which is available from the \
author."
}], "Text"]
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Cell[CellGroupData[{
Cell["1993-1996 : FeynCalc 3.0, modularization; typesetting", "Subsubsection"],
Cell["\<\
Due to the rapidly increasing amount of code, FeynCalc has been \
reorganized in a completely modular way. Each function in a package is a file \
which is loaded only on demand. For the maintainance of hundreds of packages, \
totalling 2.5 MegaByte, software engineering was needed.\
\>", "Text"],
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"\[Bullet]Special typesetting rules were added (e.g., ",
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" 3.0) . \n\n\[Bullet]Special code was written to allow new abstract \
datatypes, for example for noncommutative algebra and for special integrals."
}], "Text"],
Cell[TextData[
"\[Bullet]QCD tools for the Operator Product Expansion (OPE) were added."],
"Text"],
Cell[TextData[
"\[Bullet]Automatic Feynman rule derivation (with functional differentation) \
was coded, in order to get special Feynman rules for twist-2 (and higher) \
operators."], "Text"],
Cell["\<\
Another recent effort has been to build data bases: Convolutions, \
integrals, tensor integral transformation formulas, Feynman rules, and \
Feynman parametrizations. The newest applications include 2-loop \
spin-dependent and spin-independent Altarelli-Parisi Splitting \
functions.\
\>", "Text"]
}, Open ]]
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"A research application: The Calculation of the 2-loop Altarelli-Parisi \
Spin Splitting Functions ",
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"A non-trivial research application, where FeynCalc 3.0 (and ",
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" of course; but also FORM",
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") proved to be a useful tool, is published in the physics journal \
\"Zeitschrift f\[UDoubleDot]r Physik\" (Mertig and van Neerven 1996). High \
Energy Physics experiments (E142, E143, Hermes) measure the spin structure of \
the nucleon, described by the so-called polarized structure function ",
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" in ",
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"Editor's Note: The electronic edition of ",
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for Lorentz Algebra, Dirac Algebra, Operator handling and Feynman rule \
derivation."
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Cell[TextData[{
"The investigation of the unknown at the subatomic level is an ongoing \
adventure of human intellect and technology. Physics continues to be an \
experimental science, and thus any theory trying to explain the physical part \
of nature must be potentially falsifiable by experiment. At national and \
international high-energy accelerator laboratories, the properties of forces \
among these elementary particles are studied quantitatively by collaborations \
of typically hundreds of scientists and other specialists. FeynCalc 3.0, \
built on the new functionality of ",
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splitting functions ",
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Cell["ABOUT THE AUTHOR", "Subsection"],
Cell["ELECTRONIC SUBSCRIPTIONS", "Subsection"]
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