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arXiv · hep-th/0102115

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

N. Chepilko·A. Romanenko
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Abstract

Extended Schwinger's quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold $M$ is a homogeneous Riemannian space with the given action of isometry transformation group. Using the identification of $M$ with the quotient space $G/H$, where $H$ is the isotropy group of an arbitrary fixed point of $M$, we show that quantum mechanics on $G/H$ possesses a gauge structure, described by the gauge potential that is the connection 1-form of the principal fiber bundle $G(G/H, H)$. The coordinate representation of quantum mechanics and the procedure for selecting the physical sector of states are developed.

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N. Chepilko, A. Romanenko. 2001-02-19. Quantum mechanics on Riemannian Manifold in Schwinger's Quantization Approach II. https://doi.org/10.1007/s100520100713

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