2001/01/03 by E. A. Tagirov, Tagirov, E. A.
Chemistry · Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Geometry Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Quantum Physics (quant-ph) #gr-qc #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0101016
11 pages, LaTex 2.09-file; a talk at the 23th Symposium on Group-Theoretical Methods in Physics, Dubna, July 2000
arxiv created 2001/01/03 · openalex publication_date 2001/01/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select a single rule of quantization is proposed by requirement of a consistency of the quantum mechanics' following from the canonical and quasiclassical approaches. This rule selects also a definition of the path integration. A geometric interpretation of the noncovariance of the canonical Hamilton operator of a particle with respect to the diffeomorphisms of the Riemannian configuration space is proposed.