TRACER version 1.1: A mathematica package for γ-algebra in arbitrary dimensions

Abstract

This paper describes the first MATHEMATICA implementation of γ-algebra in arbitrary space-time dimensions according to the 't Hooft-Veltman scheme. It is the only system based on a general purpose computer algebra system treating the γ 5-problem mathematically consistently in arbitrary dimensions. The TRACER package is capable of doing just purely algebraic manipulations as well as trace operations on strings of γ-algebra objects. In addition, it provides a set of utility functions for reordering, simplifying and improving the readability of the output. Optionally the output can be obtained in a form suitable to be fed into a T EX system for high quality text processing. As a whole, the TRACER package is intended as a computerized aid to a researcher working on higher order corrections in Relativistic Quantum Field Theories. A short comparison of procedural versus rule-based programming approaches is given and the discussion is supplemented by a toy implementation of the γ-algebra in rule-based style. The paper describes in detail the usage of the TRACER package and for further illustration a correlation function of two weak currents is calculated with the aid of TRACER. Finally, data on the performance of TRACER on some common platforms are given.