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

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

2001-02-19

arxiv.org/abs/hep-th/0102115v1

Eur.Phys.J.C21:587-595,2001

Physics

High Energy Physics

High Energy Physics - Theory

18pages, no figures, LaTeX

Scientific paper

10.1007/s100520100713

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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