Nonrelativistic Limit of the Dirac-Schwarzschild Hamiltonian: Gravitational Zitterbewegung and Gravitational Spin-Orbit Coupling
We investigate the nonrelativistic limit of the gravitationally coupled Dirac equation via a Foldy-Wouthuysen transformation. The relativistic correction terms have immediate and obvious physical interpretations in terms of a gravitational Zitterbewegung and a gravitational spin-orbit coupling. We find no direct coupling of the spin vector to the gravitational force, which would otherwise violate parity. The particle-antiparticle symmetry described recently by one of us is verified on the level of the perturbative corrections accessed by the Foldy-Wouthuysen transformation. The gravitational corrections to the electromagnetic transition current are calculated.
U. D. Jentschura and J. H. Noble, "Nonrelativistic Limit of the Dirac-Schwarzschild Hamiltonian: Gravitational Zitterbewegung and Gravitational Spin-Orbit Coupling," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 88, no. 2, pp. 022121-1 - 022121-6, American Physical Society (APS), Aug 2013.
The definitive version is available at https://doi.org/10.1103/PhysRevA.88.022121
Keywords and Phrases
Dirac Equations; Electromagnetic Transitions; Foldy-Wouthuysen Transformations; Gravitational Forces; Nonrelativistic Limits; Physical Interpretation; Relativistic Correction; Spin-orbit Couplings; Linear Equations; Gravitation
International Standard Serial Number (ISSN)
Article - Journal
© 2013 American Physical Society (APS), All rights reserved.
01 Aug 2013