On Ordering of Operators in Canonical Quantization in Curved Space
arXiv:quant-ph/0101016
Abstract
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.
arXiv comment11 pages, LaTex 2.09-file; a talk at the 23th Symposium on Group-Theoretical Methods in Physics, Dubna, July 2000