A Basis for Invariants in Non-Abelian Gauge Theories

TL;DR

This paper presents an algorithm to systematically convert invariant expressions in non-Abelian gauge theories into a standard basis, facilitating computer calculations of effective actions and providing a comprehensive set of basis invariants up to dimension 16.

Contribution

It introduces a novel algorithm for expressing gauge invariants in a standard form and enumerates basis invariants up to mass dimension 16.

Findings

Algorithm successfully converts invariants into basis form

Number of basis invariants calculated up to dimension 16

Provides properties and definitions of basis invariants

Abstract

An algorithm is described to convert Lorentz and gauge invariant expressions in non--Abelian gauge theories with matter into a standard form, consisting of a linear combination of basis invariants. This algorithm is needed for computer calculations of effective actions. The defining properties of the basis invariants are reported. The number of basis invariants up to mass dimension 16 are presented.