Spin Hall effect of Photons in a Static Gravitational Field
Résumé
Starting from an Hamiltonian description of the photon through the set of Bargmann-Wigner equations, we derive new semiclassical equations of motion for the photon propagating in static gravitational field. These equations which are obtained in the representation where we could diagonalize the Hamiltonian at the order $\hbar$, present the first order corrections to the geometrical optic equations. This Hamiltonian shows two new kinds of magneto-torsion couplings which can be also interpreted in terms of Berry curvatures. But the most important result is that even in the absence of torsion the photon does not follow the geodesic as a consequence of an anomalous velocity term responsible for the spin Hall effect of light. Besides the velocity of light is not changed at this order of the approximation.