Uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary gravitational fields
- Russian Federal Nuclear Center--All-Russian Research Institute of Experimental Physics, Sarov, Mira 37, Nizhni Novgorod region, 607188 (Russian Federation)
Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows for describing the Dirac particles motion in arbitrary stationary gravitational fields. Second, it is proved that using the Parker weight operator and the subsequent transition to the {eta} representation gives the transformation of the Schroedinger equation for the nonstationary metric, when the evolution operator becomes self-conjugate. The scalar products in the {eta} representation are flat, which makes possible the use of a standard apparatus for the Hermitian quantum mechanics. Based on the results of this paper the authors draw a conclusion about solution of the problem of uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary gravitational fields including those dependent on time. The general approach is illustrated by the example of Dirac Hamiltonians for several stationary metrics, as well as for the cosmologically flat and the open Friedmann models.
- OSTI ID:
- 21502625
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 83, Issue 10; Other Information: DOI: 10.1103/PhysRevD.83.105002; (c) 2011 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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HAMILTONIANS
HERMITIAN OPERATORS
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METRICS
QUANTUM MECHANICS
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SCHROEDINGER EQUATION
TRANSFORMATIONS
DIFFERENTIAL EQUATIONS
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