Semiclassical dynamics of Dirac particles interacting with a static gravitational field |
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Authors: | Pierre Gosselin Alain Bérard Hervé Mohrbach |
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Institution: | 1. Université Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathématiques, BP74, 38402 Saint Martin d''Hères, Cedex, France;2. Université Paul Verlaine, Institut de Physique, ICPMB1-FR CNRS 2843, Laboratoire de Physique Moléculaire et des Collisions, 1, boulevard Arago, 57078 Metz, France |
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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. |
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