Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field

Abstract

The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy-Wouthuysen transformation which diagonalizes at the semiclassical order the Dirac equation for an arbitrary static spacetime metric is realized. In this representation the Hamiltonian provides for a coupling between spin and gravity through the torsion of the gravitational field. In the specific case of a symmetric gravitational field we retrieve the Hamiltonian previously found by other authors. But our formalism provides for another effect, namely, the spin hall effect, which was not predicted before in this context.

References in corpus (3)

• Dissipationless Quantum Spin Current at Room Temperature
• Topological spin transport of relativistic electron
• Reply to Comment on "Berry phase correction to electron density of states in solids"

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