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

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

2001-02-21

arxiv.org/abs/hep-th/0102139v1

Eur.Phys.J.C21:369-381,2001

Physics

High Energy Physics

High Energy Physics - Theory

23pages, no figures, LaTeX

Scientific paper

10.1007/s100520100712

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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