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This article is cited in 1 scientific paper (total in 1 paper)
Quantum Mechanics in Riemannian Space: Different Approaches to Quantization of the Geodesic Motion Compared
É. A. Tagirov Joint Institute for Nuclear Research
Abstract:
We compare different approaches to the construction of the quantum mechanics of a particle in the general Riemannian space and space-time via quantization of motion along geodesic lines. We briefly review different quantization formalisms and the difficulties arising in their application to geodesic motion in a Riemannian configuration space. We then consider canonical, semiclassical (Pauli–De Witt), and Feynman (path-integral) formalisms in more detail and compare the quantum Hamiltonians of a particle arising in these models in the case of a static, topological elementary Riemannian configuration space. This allows selecting a unique ordering rule for the coordinate and momentum operators in the canonical formalism and a unique definition of the path integral that eliminates a part of the arbitrariness involved in the construction of the quantum mechanics of a particle in the Riemannian space. We also propose a geometric explanation of another main problem in quantization, the noninvariance of the quantum Hamiltonian and the path integral under configuration space diffeomorphisms.
Keywords:
quantum mechanics, Riemannian space, quantization, geodesic motion.
Received: 10.07.2002
Citation:
É. A. Tagirov, “Quantum Mechanics in Riemannian Space: Different Approaches to Quantization of the Geodesic Motion Compared”, TMF, 136:2 (2003), 209–230; Theoret. and Math. Phys., 136:2 (2003), 1077–1095
Linking options:
https://www.mathnet.ru/eng/tmf227https://doi.org/10.4213/tmf227 https://www.mathnet.ru/eng/tmf/v136/i2/p209
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Abstract page: | 463 | Full-text PDF : | 244 | References: | 40 | First page: | 2 |
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