Analysis of the consistency of parity-odd nonbirefringent modified Maxwell theory

TL;DR

This paper investigates the properties and consistency of a parity-odd, Lorentz-violating extension of quantum electrodynamics, demonstrating that it approaches standard QED for small Lorentz-violating parameters and remains physically consistent.

Contribution

It provides a detailed analysis of the microcausality, unitarity, and scattering processes in the parity-odd nonbirefringent modified Maxwell theory coupled to fermions, establishing its consistency.

Findings

The theory maintains microcausality and unitarity.

Numerical analysis shows the theory approaches standard QED for small Lorentz violation.

The theory offers a well-defined parity-odd extension of QED.

Abstract

There exist two deformations of standard electrodynamics that describe Lorentz symmetry violation in the photon sector: CPT-odd Maxwell-Chern-Simons theory and CPT-even modified Maxwell theory. In this article, we focus on the parity-odd nonbirefringent sector of modified Maxwell theory. It is coupled to a standard Dirac theory of massive spin-1/2 fermions resulting in a modified quantum electrodynamics (QED). This theory is discussed with respect to properties such as microcausality and unitarity, where it turns out that these hold. Furthermore, a priori, the limit of the theory for vanishing Lorentz-violating parameters seems to be discontinuous. Since it is not clear, whether this is a gauge artifact, the cross section for a physical process - modified Compton scattering - is calculated numerically. Despite the numerical instabilities occurring for scattering of unpolarized electrons off polarized photons in the second physical polarization state, it is shown that for Lorentz-violating parameters much smaller than 1 the modified theory approaches standard QED, which is strengthened by analytical investigations. Hence, the theory proves to be consistent, at least with regard to the investigations performed. This leads to the interesting result of having a well-defined parity-odd extension of QED.