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arXiv · hep-th/0102139

Quantum mechanics on Riemannian Manifold in Schwinger's Quantization Approach I

N. Chepilko·A. Romanenko
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Abstract

Schwinger's quantization scheme is extended in order to solve the problem of the formulation of quantum mechanics on a space with a group structure. The importance of Killing vectors in a quantization scheme is showed. Usage of these vectors provides algebraic properties of operators to be consistent with the geometrical structure of a manifold. The procedure of the definition of the quantum Lagrangian of a free particle and the norm of velocity (momentum) operators is given. These constructions are invariant under a general coordinate transformation. The unified procedure for constructing the quantum theory on a space with a group structure is developed. Using it quantum mechanics on a Riemannian manifold with a simply transitive group acting on it is investigated.

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N. Chepilko, A. Romanenko. 2001-02-21. Quantum mechanics on Riemannian Manifold in Schwinger's Quantization Approach I. https://doi.org/10.1007/s100520100712

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