Finsler Spinoptics

Abstract

The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan connection used in this work. Then, the principles of Finslerian spinoptics are formulated on the grounds of previous work on Riemannian spinoptics, and relying on the generic coadjoint orbits of the Euclidean group. A new presymplectic structure on the indicatrix-bundle is introduced, which gives rise to a foliation that significantly departs from that generated by the geodesic spray, and leads to a specific anomalous velocity, due to the coupling of spin and the Cartan curvature, and related to the optical Hall effect.