On Ordering of Operators in Canonical Quantization in Curved Space

E. A. Tagirov

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On Ordering of Operators in Canonical Quantization in Curved Space

E. A. Tagirov

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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.

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E. A. Tagirov. 2001-01-03. On Ordering of Operators in Canonical Quantization in Curved Space. https://arxiv.org/abs/quant-ph/0101016

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