Looking for a relativistic crystal optics

Causal structure and algebraic classification of non-dissipative linear optical media

“…The algebraic classification of area metrics performed in the following sections thus becomes a geometric classification of optical materials. Through relation (41) each optical material will be associated with a unique normal form of its area metric; this completes the programme of [31].…”

“…If it is not clear from the indices that we use the Petrov notation of an object Γ we write Petrov(Γ). In four dimensions for instance, which is the case of direct physical interest, we have index pairs [01], [02], [03], [12], [31], and [23] with the corresponding Petrov indices A = 1, …, 6. The independent components of an area metric G in four dimensions may hence be arranged as the 6 × 6 Petrov matrix 2 6 6 6 6 6 6 4 3 7 7 7 7 7 7 5 ð2Þ with the components under the diagonal filled by symmetry.…”

Relativistic nature of a magnetoelectric modulus ofCr2O3crystals: A four-dimensional pseudoscalar and its measurement

“…It is called relativistic, since it occurs in the context of the relativistic (E, B) system, see (32).…”

“…Among the 122 Heesch-Shubnikov point groups 58 ones are permitting the linear magnetoelectric effect [70], and therefrom 32 ones possess diagonal components of the magnetoelectric tensor α [8,69,72]. Strictly speaking, our magnetoelectric tensor rel α in (47) belongs to the EB scheme, see (32) and (33), whereas the corresponding tensor in the literature [73] is the one of the EH scheme. However, as we can see in (47), because of µ ≈ 1 the differences are marginal and don't touch our arguments.…”

“…By comparing (32) and (33) with the above equations ( 29) to ( 31) and ( 26) to (28), we can read off the permittivity…”