Birefringence in non-linear electrodynamics emerging from a Lorentz-symmetry violation scenario

Abstract

In this paper, we investigate the classical properties of a non-linear electrodynamics that emerges from one loop effective action for fermions coupled to an antisymmetric background tensor, that breaks the Lorentz symmetry in the model. The conservation laws are obtained through the Belinfante-Rosenfeld energy-momentum tensor in the non-linear electrodynamics that provides the energy density, the Poynting vector, the linear momentum and the stress tensor. In particular, this Lorentz symmetry violation breaks the symmetric index of the energy-momentum tensor, but it preserves the gauge invariance, as we expect. We introduce the prescription of a magnetic background field, that we consider constant and uniform. For propagation effects, the model is linearized by the magnetic background. This prescription allows us investigations of the plane wave propagation in the presence of an external magnetic field. In this context, we obtain the constitutive relations of the material medium, that behaves like an bi-anisotropic medium. Thereby, we calculate the refractive index whose one of the solutions show the total absorption of the wave in the medium. Using the wave equation for linear polarization, we investigate the birefringence phenomenon when the linear wave polarization changes with the magnetic background direction. The birefringence is so related to one of the spatial component of the LSV tensor in which we estimate through the PVLS experiment. We use one of the dispersion relations to obtain the kinematic of the Compton effect in the presence of the LSV parameter.