Problems with Lorentz Violation Originating From a Cosmologically Varying Pseudoscalar Field

TL;DR

This paper investigates Lorentz and CPT violation caused by a cosmologically varying pseudoscalar field, revealing instabilities and potential energy loss mechanisms that challenge the consistency of such models.

Contribution

It analyzes the stability and behavior of Lorentz-violating electrodynamics with a pseudoscalar field, highlighting issues in perturbative solutions and implications for energy conservation.

Findings

Singularities appear in perturbative field expansions.

Nonperturbative approaches partially resolve issues.

Energy loss via Cerenkov-like radiation may prevent uniform charge motion.

Abstract

Lorentz- and CPT-violating models of electrodynamics with Chern-Simons terms are typically plagued by various sorts of instabilities. However, when the Chern-Simons term arises from a slow time variation in a pseudoscalar field with an axion-like electromagnetic coupling, the total energy of the theory is bounded below. We examine the behavior of such a theory, finding that in a systematic power series expansion of the magnetic and pseudoscalar fields, singularities appear in the field profiles. Some of the questionable behavior can be cured by taking a fully nonperturbative approach, but other problematic terms remain. This may be an indication that Cerenkov-like radiation will automatically carry away energy from a moving charge, preventing a charge from moving with uniform velocity over extended distances.