Classical Solutions in a Lorentz-violating Maxwell-Chern-Simons Electrodynamics

TL;DR

This paper investigates classical solutions in a Lorentz-violating Maxwell-Chern-Simons model derived from higher-dimensional theories, revealing background-dependent deviations and anisotropic effects in electromagnetic behavior.

Contribution

It introduces and analyzes classical solutions in a Lorentz-violating planar Maxwell-Chern-Simons model, highlighting deviations from standard theory due to background fields.

Findings

Background-dependent correction terms dominate at large distances in time-like case.

Solutions exhibit spatial anisotropy in space-like case.

Deviations from usual MCS Electrodynamics are observed.

Abstract

We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carroll-Field-Jackiw term. We then write and study the extended Maxwell equations and the corresponding wave equations for the potentials. The solution to these equations show some interesting deviations from the usual MCS Electrodynamics, with background-dependent correction terms. In the case of a time-like background, the correction terms dominate over the MCS sector in the region far from the origin, and establish the behaviour of a massless Electrodynamics (in the electric sector). In the space-like case, the solutions indicate the clear manifestation of spatial anisotropy, which is consistent with the existence of a privileged direction is space.