Discrete symmetry transformations on non-abelian gauge fields

TL;DR

This paper investigates how discrete symmetries like time-reversal and charge conjugation act on non-abelian gauge fields, revealing dependence on generator choices and proposing unified transformation rules.

Contribution

It introduces generator-independent transformation rules for non-abelian gauge bosons under discrete symmetries, resolving ambiguities in their transformation properties.

Findings

Transformation rules depend on generator choice

Unified rules can be constructed using matrix forms

Generator-independent transformations are achievable

Abstract

All gauge bosons of a non-abelian gauge theory do not transform the same way under the discrete transformations of time-reversal and charge-conjugation. Moreover, the transformations rules depend on how the generators are chosen. We show how well-defined rules pertain only to specific choices of generators, and then show how unified rules can be constructed, using matrix forms of the gauge bosons, which are completely independent of the choice of generators.