Photon propagator in skewon electrodynamics

Abstract

Electrodynamics with a local and linear constitutive law is used as a framework for models violating Lorentz covariance. The constitutive tensor of such a construction is irreducibly decomposed into three independent pieces. The principal part is the anisotropic generalisation of the standard electrodynamics. The two other parts, axion and skewon, represent non-classical modifications of electrodynamics. We derive the expression for the photon propagator in the Minkowski spacetime endowed with a skewon field. For a relatively small (antisymmetric) skewon field, a modified Coulom law is exhibited.

Electromagnetic potential in pre-metric electrodynamics: Causal structure, propagators and quantization

“…Using the second adjoint for the derivation of the quasi-inverse follows ideas by Itin [12] and, more recently, [13]. The same author showed [11][12][13] that the adjugate of M is given by…”

“…It follows from the properties of the quantum field A, that an admissible n-point distribution ω n must be a weak solution of the field equation in each argument 13 We denote the complex conjugate of z byz. 14 The "natural" topology of A is that induced (via the direct sum, quotient and subspace topology) by the test function topology on Ω 3 c ðMÞ.…”

“…Observe that directly from (31) follows M ab m b ¼ κ a − κ 0a , so that, given two of m; κ; κ 0 , we can recover the third. These gauge transformations of the quasi-inverse fit in the structure of gauge transformations Itin found for the photon propagator in linear response media [13]. Looking at the Maxwell case (26), we notice that (31) is exactly the photon propagator transformation Eq.…”

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

“…It is important in quantum field theoretical extension of electrodynamics. It was derived and applied to axion and skewon modified electrodynamics by Itin [30], [32], [40]. In a similar way, Andrianov et al [1] studied the propagation of photons and massive vector mesons in the presence of a medium, which violates Lorentz and a CPT invariance.…”

“…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].…”