New Effects in the Vicinity of a Perfectly Conducting Plate in a Non-minimal Lorentz Violation Scenario

Abstract

In this paper we consider some physical phenomena in the vicinity of a conducting plate in a non-minimal Lorentz-violating scenario in 3 + 1 dimensions. We consider a model where the dynamics of the abelian gauge field is given by the standard Maxwell Lagrangian added by a Lorentz symmetry breaking term with the presence of higher order derivatives in the gauge field. The Lorentz symmetry breaking is due to the presence of a single background vector dλ and we perform the calculations perturbatively up to first order in dλ. We obtain the propagator for the gauge field in the presence of a mirror and the interaction force between the mirror and a point-like electric charge, as well as the interaction force between the mirror and an electric dipole. We show that, on the contrary to what happens in a minimal Lorentz-violating scenario with one single background field (L.H.C. Borges, F.A. Barone, Eur. Phys. J. C 693, 77, 2017), the image method is not valid in the model that we consider in this paper. As a consequence, the symmetry of spatial reflection on the mirror is broken. We also investigate the emergence of a torque in a system composed by a mirror and a point-like electric charge, placed at a fixed distance apart each other. The results obtained in this work have no counterpart in the Maxwell electrodynamics and were not verified in any Lorentz-violating scenario previously.