A perfectly conducting surface in electrodynamics with Lorentz symmetry breaking

Abstract

In this paper we consider a model which exhibits explicit Lorentz symmetry breaking due to the presence of a single background vector vμ coupled to the gauge field. We investigate such a theory in the vicinity of a perfectly conducting plate for different configurations of vμ. First we consider no restrictions on the components of the background vector and we treat it perturbatively up to second order. Next, we treat vμ exactly for two special cases: the first one is when it has only components parallel to the plate, and the second one when it has a single component perpendicular to the plate. For all these configurations, the propagator for the gauge field and the interaction force between the plate and a point-like electric charge are computed. Surprisingly, it is shown that the image method is valid in our model and we argue that it is a non-trivial result. We show there arises a torque on the mirror with respect to its positioning in the background field when it interacts with a point-like charge. It is a new effect with no counterpart in theories with Lorentz symmetry in the presence of a perfect mirror.