SIM$(1)$--VSR Maxwell-Chern-Simons electrodynamics

TL;DR

This paper introduces a VSR-inspired generalization of Maxwell-Chern-Simons electrodynamics, revealing significant nonlocal effects that alter classical solutions and produce a finite static potential between charges.

Contribution

It develops a novel VSR-based extension of MCS electrodynamics, analyzing its gauge symmetry, classical solutions, and static potential with nonlocal effects.

Findings

VSR effects significantly modify the classical electric field.

The static energy and potential between charges are finite due to VSR effects.

The model exhibits departures from standard MCS theory with new physical implications.

Abstract

In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM$(1)$--VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and health departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges are derived and we show that the VSR effects play an important part in obtaining a (novel) finite expression for the static potential.