Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field

TL;DR

This paper develops a semiclassical framework for Dirac particles in static gravitational fields, revealing a spin-gravity coupling and predicting a novel spin Hall effect.

Contribution

It introduces a Foldy-Wouthuysen transformation for Dirac particles in static spacetimes, uncovering a new spin Hall effect not previously predicted.

Findings

Identifies a spin-gravity coupling via torsion.

Recovers known Hamiltonian for symmetric fields.

Predicts a new spin Hall effect.

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.