Package for calculations and simplifications of expressions with Dirac matrices (MatrixExp)

Abstract

This paper describes a package for calculations of expressions with Dirac matrices. Advantages over existing similar packages are described. MatrixExp package is intended for simplification of complex expressions involving γ-matrices, providing such tools as automatic Feynman parameterization, integration in d-dimensional space, sorting and grouping of results in a given order. Also, in comparison with the existing similar package Tracer, the presented package MatrixExp has more enhanced input possibility. User-available functions of MatrixExp package are described in detail. Also an example of calculation of Feynman diagram for process b → s γ g with application of functions of MatrixExp package is presented. Program summary Title of program:MatrixExp Catalogue identifier:ADWB Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWB Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Programming language:MATHEMATICA Computer:PC Pentium Operating system:Windows No. of lines in distributed program, including test data, etc.: 1551 No. of bytes in distributed program, including test data, etc.: 16 040 Distribution format:tar.gz RAM:loading the package uses approx. 3 500 000 bytes of RAM. However memory required for calculations depends heavily on the expressions in the view, as the package uses recursive functions, and MATHEMATICA dynamically allocates memory. Package has been tested to work on PC Pentium II 233 MHz with 128 Mb of memory calculating typical diagrams of contemporary calculations. Nature of problem:Feynman diagram calculation, simplification of expressions with γ-matrices Solution method:Analytic transformations, dimensional regularization, Feynman parameterization Restrictions:MatrixExp package works only with single line of expressions (G[l1, … ]), in contrast to the Tracer package that works with multiple lines, i.e., the following is possible in Tracer, but not in MatrixExp: G[l1, … ]**G[l2, … ]**G[l3, … ] … , which will return the result of G[l1, … ]**G[l1, … ]**G[l1, … ]…. Unusual features:none Running time:Seconds for expressions with several different γ-matrices on Pentium IV 1.8 GHz and of the order of a minute on Pentium II 233 MHz. Calculation times rise with the number of matrices.