Material boundaries in Carroll–Field–Jackiw Lorentz-violating electrodynamics

This paper investigates certain aspects of the CPT-odd photon sector of the minimal Standard Model Extension (SME) in the presence of a perfectly conducting plate (perfect mirror). The considered sector is described by Carroll–Field–Jackiw (CFJ) electrodynamics, where Lorentz violation is due to the presence of a single background vector denoted as kAFμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( k_{AF}\right) ^{\mu }$$\end{document}, which we treat perturbatively up to second order. Specifically, we derive the modified propagator for the electromagnetic field due to the presence of the perfect mirror, and we study the corresponding interaction between the mirror and a stationary point-like charge. Our results reveal that when the charge is positioned near the mirror, a spontaneous torque emerges, which is a unique effect of Lorentz symmetry breaking. Additionally, we demonstrate that the image method for this theory is applicable when the background vector has only the component perpendicular to the mirror.