On skewon modification of light cone structure

TL;DR

This paper explores how skewon modifications in electromagnetic media can lead to extreme Lorentz symmetry violations, affecting light cone structures and dispersion relations in a covariant, metric-free framework.

Contribution

It introduces a canonical decomposition of the optic tensor into principle and skewon parts, revealing new Lorentz violation phenomena and detailed analysis of skewon types and their effects.

Findings

Skewon modifications cause all solutions to be spacelike or null, indicating extreme Lorentz violation.

Detailed analysis of antisymmetric and symmetric skewon cases, uncovering new phenomena.

Parametric gap in symmetric skewon models resembles Higgs-like behavior.

Abstract

Electromagnetic media with generic linear response provide a rich class of Lorentz violation models. In the framework of a general covariant metric-free approach, we study electromagnetic wave propagation in these media. We define the notion of an optic tensor and present its unique canonical irreducible decomposition into the principle and skewon parts. The skewon contribution to the Minkowski vacuum is a subject that does not arise in the ordinary models of Lorentz violation based on a modified Lagrangian. We derive the covector parametrization of the skewon optic tensor and discuss its $U(1)$-gauge symmetry. We obtain several compact expressions for the contribution of the principle and skewon optic tensor to the dispersion relation. As an application of the technique proposed here, we consider the case of a generic skewon tensor contributed to a simple metric-type principle part. Our main result: Every solution of the skewon modified Minkowski dispersion relation is necessary spacelike or null. It provides an extreme violation of the Lorentz symmetry. The case of the antisymmetric skewon is studied in detail and some new special cases (electric, magnetic, and degenerate) are discovered. In the case of a skewon represented by a symmetric matrix, we observe a parametric gap that has some similarity to the Higgs model. We worked out a set of specific examples that justify the generic properties of the skewon models and demonstrate the different types of the Lorentz violation phenomena.