Skewon modification of the light cone structure

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.

Photon propagator in skewon electrodynamics

“…For the antisymmetric tensor Q ij , we can derive from (4.11) a simple representation, see [32]. Indeed, the expression…”

“…see [32] for details and proofs. Here the term λ 0 q i q j is the adjoint of the principal part matrix P ij alone.…”

“…We use the parametrization given in [32]. Moreover, we consider a special 3-parametric skewon of the "electric" type…”

“…In [32], we presented a new form of dispersion relation in the skewon sector of the premetric electrodynamics and derive some new features of this model, such as superluminal wave propagation and Higgs-type symmetry breaking. The analysis given in [31], [32], [33], [34], and [36] was restricted to the wave propagation problems, i.e., to the vacuum case. In the present paper, we extend this analysis to the nonempty regions and derive the explicit expression of the skewon modified photon propagator (Green's function in the momentum representation).…”

Generally covariant Maxwell theory for media with a local response: Progress since 2000

“…2) Skewon part of the electromagnetic response tensor: The general concept of the skewon part of the response tensor was introduced in [17], for its relation to dissipation, see [18]. The effects of the skewon on light propagation were studied by Itin, Ni, Obukhov, et al [62], [36], [40], [53], [58], [38], [37], [56]. A theory of the skewon in interaction with the gravitational field was provided in [23].…”