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Nonrelativistic Limit Of The Dirac-Schwarzschild Hamiltonian: Gravitational Zitterbewegung And Gravitational Spin-Orbit Coupling, Ulrich D. Jentschura, J. H. Noble
Nonrelativistic Limit Of The Dirac-Schwarzschild Hamiltonian: Gravitational Zitterbewegung And Gravitational Spin-Orbit Coupling, Ulrich D. Jentschura, J. H. Noble
Physics Faculty Research & Creative Works
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.
Gravitationally Coupled Dirac Equation For Antimatter, Ulrich D. Jentschura
Gravitationally Coupled Dirac Equation For Antimatter, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences ("surprises") related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously by Brill and Wheeler [Rev. Mod. Phys. 29, 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion of the curved-space Dirac equation from the so-called "East-Coast" to the "West-Coast" convention, in order to bring the gravitationally coupled Dirac equation to a form where it can easily …