From Dirac Theories in Curved Space-Times to a Variation of Dirac's Large-Number Hypothesis
Space-time quantization is not necessary in order to combine general relativity and quantum mechanics. Indeed, before we could ever conceive to observe effects due to space-time quantization, we should first consider the leading-order coupling of the Dirac particle to a curved spacetime. Space-time curvature is visible on the classical level, and can be treated on the classical level. Deviations from perfect Lorentz symmetry caused by effects other than space-time curvature may result in conceivable anisotropies of spacetime. Key to the calculation of the gravitational coupling of Dirac particles is the observation that the Dirac Clifford algebra needs to be augmented to include the local character of the space-time metric. Recent developments in this field include a series of papers where the gravitationally coupled Dirac particle is formulated first in a fully relativistic setting, and then, a generalized Foldy-Wouthuysen transformation is applied in order to isolate the nonrelativistic limit, plus correction terms.
U. D. Jentschura, "From Dirac Theories in Curved Space-Times to a Variation of Dirac's Large-Number Hypothesis," Annalen der Physik, vol. 526, no. 5-6, pp. A47-A50, Wiley-Blackwell, Jul 2014.
The definitive version is available at https://doi.org/10.1002/andp.201400808
Keywords and Phrases
Quantum Theory; Relativity; Clifford Algebra; Correction Terms; Curved Spacetime; Dirac Particles; Foldy-Wouthuysen Transformations; General Relativity; Nonrelativistic Limits; Space-time Metric; Radio Communication
International Standard Serial Number (ISSN)
Article - Journal
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01 Jul 2014