Consistency analysis of a CPT-even and CPT-odd lorentz-violating effective field theory in the electrodynamics at Planck scale by an influence of a background isotropic field

TL;DR

This paper investigates the effects of Lorentz invariance violation in electrodynamics at the Planck scale, proposing a new formalism that includes CPT-even and CPT-odd modifications, and analyzes their stability, causality, and unitarity.

Contribution

It introduces a novel formalism for LIV in electrodynamics with high derivative terms and background fields, analyzing CPT properties and their physical consistency.

Findings

CPT-even modifications preserve stability, causality, and unitarity.

CPT-odd modifications violate causality and unitarity due to vacuum birefringence.

The framework helps identify viable LIV models at high energies.

Abstract

Based on the motivation that some quantum gravity theories predicts the Lorentz Invariance Violation (LIV) around Planck-scale energy levels, this paper proposes a new formalism that addresses the possible effects of LIV in the electrodynamics. This formalism is capable of changing the usual electrodynamics through high derivative arbitrary mass dimension terms that includes a constant background field controlling the intensity of LIV in the models, producing modifications in the dispersion relations in a manner that is similar to the Myers-Pospelov approach. With this framework, it was possible to generate a CPT-even and CPT-odd generalized modifications of the electrodynamics in order to study the stability and causality of these theories considering the isotropic case for the background field. An additional analysis of unitarity at tree level was considered by studying the saturated propagators. After this analysis, we conclude that, while CPT-even modifications always preserves the stability, causality and unitarity in the boundaries of the effective field theory and therefore may be good candidates for field theories with interactions, the CPT-odd one violates causality and unitarity. This feature is a consequence of the vacuum birefringence characteristics that are present in CPT-odd theories for the photon sector.