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This article is cited in 4 scientific papers (total in 4 papers)
General-covariant quantum mechanics in Riemannian space-time III. Dirac's particle
É. A. Tagirov Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
Abstract:
A general covariant analog of the standard non-relativistic Quantum Mechanics with relativistic corrections in normal geodesic frames in the general Riemannian space-time is constructed for the Dirac particle. Not only the Pauli equation with hermitean hamiltonian and the pre-Hilbert structure of space of its solutions but also the matrix elements of hermitean operators of momentum, (curvilinear) spatial coordinates and spin of the particle are deduced as general-covariant asymptotic approximation in $c^{-2}$, $c$ being the velocity of light, to their naturally determined general-relativistic pre-images. It is shown that the hamiltonian in the Pauli equation originated by the Dirac equation is unitary equivalent to the operator of energy,
originated by the metric energy-momentum tensor of the spinor field. Commutation and other properties of the observables connected with the considered change of geometrical background
of Quantum Mechanics are briefly discussed.
Received: 15.12.1994
Citation:
É. A. Tagirov, “General-covariant quantum mechanics in Riemannian space-time III. Dirac's particle”, TMF, 106:1 (1996), 122–132; Theoret. and Math. Phys., 106:1 (1996), 99–107
Linking options:
https://www.mathnet.ru/eng/tmf1102https://doi.org/10.4213/tmf1102 https://www.mathnet.ru/eng/tmf/v106/i1/p122
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