Quantum Mechanics in Curved Configurational Space
| dc.creator | Tagirov, E. A. | |
| dc.date | 2002-12-18 | |
| dc.date.accessioned | 2026-07-07T03:27:26Z | |
| dc.date.available | 2026-07-07T03:27:26Z | |
| dc.description | Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the Rimannian configurational spaces. A unique rule of ordering of operators in the canonical formalism and a unique definition of the path integral are established and, thus, a part of ambiguities in the quantum counterpart of geodesic motion is removed. A geometric interpretation is proposed for non-invariance of the quantum mechanics on coordinate transformations. An approach alternative to the quantization of geodesic motion is surveyed, which starts with the quantum theory of a neutral scalar field. Consequences of this alternative approach and the three formalisms of quantization are compared. In particular, the field theoretical approach generates a deformation of the canonical commutation relations between coordinates and momenta of a prticle. A possible cosmological consequence of the deformation is presented in short. Key words: quantum mechanics, Riemannian space, geodesic motion, deformation. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0212076 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0212076 | |
| dc.identifier | Int.J.Theor.Phys. 42 (2003) 465-497 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/34430 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Quantum Mechanics in Curved Configurational Space | |
| dc.type | text |