Marius -Adrian Oancea
The propagation of test fields on a fixed Lorentzian manifold is often studied by using the geometrical optics approximation. In the limit of infinitely high frequencies, the geometrical optics approximation provides a conceptual transition between the test field and an effective point-particle description. The corresponding point-particles follow the geodesics of the underlying spacetime. However, the geometrical optics approximation gradually breaks down as test fields of finite frequency are considered. In this thesis, we consider the propagation of test fields on spacetime, beyond the leading-order geometrical optics approximation. By performing a covariant Wentzel-Kramers-Brillouin analysis for test fields, we show how higher-order corrections to the geometrical optics approximation can be considered. We obtain an effective point-particle description, which contains spin-dependent corrections to the geodesic motion. This represents a covariant generalization of the well-known spin Hall effect, usually studied and observed in condensed matter physics and in optics.
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