Lorentz and CPT symmetries in commutative and noncommutative spacetime

TL;DR

This paper examines whether Lorentz and CPT symmetries are violated in a fermionic gauge theory, finding no evidence of such violations in both commutative and noncommutative spacetime through explicit calculations.

Contribution

It provides a detailed calculation showing that radiative corrections do not induce Lorentz and CPT violation in the studied theory, clarifying their status in different spacetime frameworks.

Findings

No Lorentz and CPT violation detected in the model

Radiative corrections do not generate Chern-Simons-like terms

Results hold in both commutative and noncommutative spacetime

Abstract

We investigate the fermionic sector of a given theory, in which massive and charged Dirac fermions interact with an Abelian gauge field, including a non standard contribution that violates both Lorentz and CPT symmetries. We offer an explicit calculation in which the radiative corrections due to the fermions seem to generate a Chern-Simons-like effective action. Our results are obtained under the general guidance of dimensional regularization, and they show that there is no room for Lorentz and CPT violation in both commutative and noncommutative spacetime.