Wave propagation in axion electrodynamics

TL;DR

This paper explores how axion fields influence electromagnetic wave propagation within a covariant, premetric formalism, revealing unique birefringence effects and modifications to light cone structures that suggest Lorentz violation.

Contribution

It embeds axion electrodynamics into a premetric Maxwell framework, deriving a covariant dispersion relation and analyzing wave behavior for various axion field configurations.

Findings

Birefringence signals Lorentz violation in axion electrodynamics.

Axion fields modify the topology of light cone surfaces.

Optical metrics are non-pseudo-Riemannian and non-Finslerian.

Abstract

In this paper, the axion contribution to the electromagnetic wave propagation is studied. First we show how the axion electrodynamics model can be embedded into a premetric formalism of Maxwell electrodynamics. In this formalism, the axion field is not an arbitrary added Chern-Simon term of the Lagrangian, but emerges in a natural way as an irreducible part of a general constitutive tensor.We show that in order to represent the axion contribution to the wave propagation it is necessary to go beyond the geometric approximation, which is usually used in the premetric formalism. We derive a covariant dispersion relation for the axion modified electrodynamics. The wave propagation in this model is studied for an axion field with timelike, spacelike and null derivative covectors. The birefringence effect emerges in all these classes as a signal of Lorentz violation. This effect is however completely different from the ordinary birefringence appearing in classical optics and in premetric electrodynamics. The axion field does not simple double the ordinary light cone structure. In fact, it modifies the global topological structure of light cones surfaces. In CFJ-electrodynamics, such a modification results in violation of causality. In addition, the optical metrics in axion electrodynamics are not pseudo-Riemannian. In fact, for all types of the axion field, they are even non-Finslerian.