Relativistic electrodynamics of continuous media

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Abstract
The relativistic transform of electromagnetic fields and inductions in a nonlinear medium is studied theoretically, within the framework of classical electrodynamics. A covariant formulation of the electrodynamics of nonlinear media is presented. This theoretical formulation is of particular relevance to periodic systems since the spatial symmetries of a given medium, which determine most of its linear and nonlinear electromagnetic properties, as described by group theory are not conserved by the Lorentz transform (space-time symmetry). The Čerenkov radiation process is treated as an example in the rest frame of the interacting electron; it is found that in this case the linear refractive index of the dielectric medium becomes anisotropic and exhibits a singularity at the usual Čerenkov radiation angle.

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