Classical Solutions in a Lorentz-violating Scenario of Maxwell-Chern-Simons-Proca Electrodynamics

TL;DR

This paper investigates classical solutions in a Lorentz-violating Maxwell-Chern-Simons-Proca model derived from a dimensional reduction, revealing background-dependent effects and anisotropies in the solutions.

Contribution

It provides exact solutions for purely timelike backgrounds and approximate solutions for spacelike backgrounds, highlighting Lorentz-violating effects in the extended model.

Findings

Exact algebraic solutions for timelike backgrounds.

Approximate solutions show spatial anisotropy.

Solutions resemble standard MCS-Proca behavior at large distances.

Abstract

Taking as starting point the planar model arising from the dimensional reduction of the Abelian-Higgs Carroll-Field-Jackiw model, we write down and study the extended Maxwell equations and the corresponding wave equations for the potentials. The solutions for these equations correspond to the usual ones for the MCS-Proca system, supplemented with background-dependent correction terms. In the case of a purely timelike background, exact algebraic solutions are presented which possess a similar behavior to the MCS-Proca counterparts near and far from the origin. On the other hand, for a purely spacelike background, only approximate solutions are feasible. They consist of non-trivial analytic expressions with a manifest evidence of spatial anisotropy, which is consistent with the existence of a privileged direction in space. These solutions also behave similarly to the MCS-Proca ones near and far from the origin.