Symbolic Algebra and Renormalization of Gauge Theories

TL;DR

This paper presents a computational scheme using Mathematica for symbolic algebra in gauge theory renormalization, enabling efficient two-loop calculations of renormalization group functions and simplifying electroweak expressions.

Contribution

It introduces a new scheme for representing and manipulating gauge theory objects in symbolic algebra software, facilitating complex perturbative calculations.

Findings

Calculated two-loop renormalization group functions for SU(m) gauge theories with massless fermions.

Simplified two-loop electroweak calculation expressions.

Demonstrated the scheme's efficiency using Mathematica.

Abstract

Symbolic algebra relevant to the renormalization of gauge theories can be efficiently performed by machine using modern packages. We devise a scheme for representing and manipulating the objects involved in perturbative calculations of gauge theories. This scheme is readily implemented using the general purpose package, Mathematica. The techniques discussed are used to calculate renormalization group functions for a non-abelian $SU(m)$ gauge theory with massless fermions in a representation R, in the two-loop approximation, and to simplify some expressions arising in electroweak calculations at the two loop level.