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Particles and Fields

Eur. Phys. J. C 21, 587-595 (2001)
DOI: 10.1007/s100520100713

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

N.M. Chepilko1 and A.V. Romanenko2

1  Physics Institute of the Ukrainian Academy of Sciences, Kyiv-03 028, Ukraine
2  Kyiv Taras Shevchenko University, Department of Physics, Kyiv-03 022, Ukraine

(Received: 27 June 2000 / Revised version: 10 May 2001 / Published online: 19 July 2001 -© Springer-Verlag / Società Italiana di Fisica 2001 )

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.

© Società Italiana di Fisica, Springer-Verlag 2001