Semi-transparent boundaries in CPT-even Lorentz violating electrodynamics

TL;DR

This paper explores how semi-transparent boundaries affect electromagnetic interactions in a Lorentz-violating framework, revealing novel effects like spontaneous torque near mirrors, with potential extensions to more general backgrounds.

Contribution

It introduces a perturbative analysis of CPT-even Lorentz violation effects on electromagnetic fields near semi-transparent mirrors, uncovering new phenomena such as torque on charges.

Findings

Spontaneous torque appears near semi-transparent mirrors in Lorentz-violating electrodynamics.

The modified propagator and interactions are computed up to second order in Lorentz-violating parameters.

Results recover classical image method in the perfect mirror limit.

Abstract

Some aspects of the nonbirefringent CPT-even gauge sector of the Standard Model Extension (SME), in the vicinity of a semi-transparent mirror, are investigated in this paper. We first consider a model where the Lorentz symmetry breaking is caused by a single background vector $v^{\mu}$, and we obtain perturbative results up to second order in $v^{\mu}$. Specifically, we compute the modified propagator for the gauge field due to the presence of the mirror and we analyze the corresponding interaction between the mirror and a stationary point-like charge. We show that when the charge is placed in the vicinity of the mirror, a spontaneous torque emerges, which is a new effect with no counterpart in Maxwell electrodynamics. We also compare these results with the corresponding ones obtained for the Lorentz violating scalar field theory. As expected, in the limiting case of perfect mirrors, we recover the interaction found via the image method. Finally, we discuss how we can extend these results for a more general Lorentz violating background.