FormTracer - A Mathematica Tracing Package Using FORM

TL;DR

FormTracer is a Mathematica package that leverages FORM for high-performance tensor tracing, supporting diverse dimensions and Lie groups, with optimized algorithms to reduce redundancy and enhance efficiency.

Contribution

It introduces a flexible, user-friendly Mathematica interface for tensor tracing that combines FORM's efficiency with advanced decomposition algorithms.

Findings

High performance in tensor trace computations

Supports arbitrary space, spinor, and gauge-group dimensions

Reduces redundant calculations through decomposition algorithms

Abstract

We present FormTracer, a high-performance, general purpose, easy-to-use Mathematica tracing package which uses FORM. It supports arbitrary space and spinor dimensions as well as an arbitrary number of simple compact Lie groups. While keeping the usability of the Mathematica interface, it relies on the efficiency of FORM. An additional performance gain is achieved by a decomposition algorithm that avoids redundant traces in the product tensors spaces. FormTracer supports a wide range of syntaxes which endows it with a high flexibility. Mathematica notebooks that automatically install the package and guide the user through performing standard traces in space-time, spinor and gauge-group spaces are provided.