Nonrelativistic Limit of the Dirac–Schwarzschild Hamiltonian: Gravitational Zitterbewegung and Gravitational Spin–Orbit Coupling

Jentschura, Ulrich David and Noble, J. H. (2013) Nonrelativistic Limit of the Dirac–Schwarzschild Hamiltonian: Gravitational Zitterbewegung and Gravitational Spin–Orbit Coupling. PHYSICAL REVIEW A, 88 (2). ISSN 2469-9926

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Abstract

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 in [Phys.Rev.A 87, 032101 (2013)] 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.

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