Semiclassical analysis of Dirac fields on curved spacetime

Abstract

We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed at leading and next-to-leading order in the small expansion parameter $\hslash$. Taking into account the spin-orbit coupling between the internal and external degrees of freedom of wave packets, we derive effective ray equations with spin-dependent terms. These equations describe the gravitational spin Hall effect of localized Dirac wave packets. We treat both massive and massless Dirac fields and show how a covariantly defined Berry connection and the associated Berry curvature govern the semiclassical dynamics. The gravitational spin Hall equations are shown to be particular cases of the Mathisson-Papapetrou equations for spinning objects.

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• Spin oscillations of neutrinos scattered by the supermassive black hole in the galactic center
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• Dirac Equation with Space Contributions Embedded in a Quantum-Corrected Gravitational Field