Quantum mechanics on Riemannian manifold in Schwinger's quantization approach II

The extended Schwinger 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 an isometry transformation group. Using the identification of M with the quotient space...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2001-07, Vol.21 (3), p.587-595
Main Authors: Chepilko, N.M., Romanenko, A.V.
Format: Article
Language:English
Subjects:
Isotropy
Measurement
Quantum mechanics
Quantum physics
Quotients
Riemann manifold
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Summary:The extended Schwinger 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 an 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 a 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 the states are developed.
ISSN:1434-6044
1434-6052
DOI:10.1007/s100520100713