Geometrical optics consists of approximating the evolution of an electromagnetic wave, solution to Maxwell's equations, by ray equations. In the limit of infinite frequencies, the rays have the usual semi-classical interpretation of being the paths of photons, null geodesics. At high but finite frequencies, corrections to these rays are expected. For light propagating in a medium, these corrections have been observed. In quantum mechanics, corrections in the context of adiabatic perturbations theory are well-studied. Wigner functions belong to the tools commonly used to capture them. In this talk, I will present a covariant version of Wigner-Weyl calculus which can, at least formally, be used in relativity. Corrections to geometrical optics can then be calculated, and one recovers results previously obtained by Oancea, et al., and Andersson, et al.. The effective ray equations can be recast as massless MPD equations, with a specific supplementary condition.
Jérémie Joudioux (Golm): Covariant Weyl calculus with application to geometrical optics in relativity
