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[Licence| Download | New Version Template] acnw_v1_0.gz(8 Kbytes)
Manuscript Title: Feynmanparameter and trace - programs for expressing Feynman amplitudes as integrals over Feynman parameters.
Authors: T.H. West
Program title: FeynmanParameter[] and trace[]
Catalogue identifier: ACNW_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 77(1993)286
Programming language: Mathematica.
RAM: 4000K words
Keywords: Computer algebra, General purpose, Diagramatic expansions, Feynman parameters, Traces, Gamma matrices, Particle physics, Symbolic manipulation, Mathematica.
Classification: 4.4, 5.

Nature of problem:
Calculation of Feynman diagrams with loops - including the conversion of momentum integrals into integrals over Feynman parameters and the evaluation of any traces - in an arbitrary number of dimensions.

Solution method:
Symbolic manipulation of expressions in the Mathematica environment using algorithms given in the long write-up.

Restrictions:
FeynmanParameter can convert at most three momenta integrals into integrals over Feynman parameters at one time. Feynman diagrams with more than three loops (and thus more than three momenta integrals) can be evaluated by repeated application of FeynmanParameter. However, unless significant simplifications are made, evaluating diagrams with more than three loops is prohibatively time consuming.

Running time:
The running time depends strongly on the number of loops in the Feynman diagram that is being evaluated. The evaluation of a typical 2-loop diagram on an 80386 PC requires anywhere from one minute to a few hours depending on the details of the calculation. Of course, these times can be reduced considerably by using a computer which is more powerful than this minimum configuration.

References:
[1] S. Wolfram, Mathematica: A System for Doing Mathematics by Computer (Addison-Wesley, Reading, Maryland, 1988).