On light propagation in premetric electrodynamics: the covariant dispersion relation

Abstract

The premetric approach to electrodynamics provides a unified description of a wide class of electromagnetic phenomena. In particular, it involves axion, dilaton and skewon modifications of the classical electrodynamics. This formalism also emerges when the non-minimal coupling between the electromagnetic tensor and the torsion of Einstein–Cartan gravity is considered. Moreover, the premetric formalism can serve as a general covariant background of the electromagnetic properties of anisotropic media. In the current paper, we study wave propagation in the premetric electrodynamics. We derive a system of characteristic equations corresponded to premetric generalization of the Maxwell equation. This singular system is characterized by the adjoint matrix which turns to be of a very special form—proportional to a scalar quartic factor. We prove that a necessary condition for the existence of a non-trivial solution of the characteristic system is expressed by a unique scalar dispersion relation. In the tangential (momentum) space, it determines a fourth-order light hypersurface which replaces the ordinary light cone of the standard Maxwell theory. We derive an explicit form of the covariant dispersion relation and establish its algebraic and physical origin.