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

Using the extended Schwinger quantization approach, quantum mechanics on a Riemannian manifold M with the given action of an intransitive group of isometries is developed. It was shown that quantum mechanics can be determined unequivocally only on submanifolds of M where G acts simply transitively (...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2001-07, Vol.21 (4), p.757-767
Main Authors: Chepilko, N.M., Romanenko, A.V.
Format: Article
Language:English
Subjects:
Manifolds (mathematics)
Measurement
Quantum mechanics
Quantum physics
Riemann manifold
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Summary:Using the extended Schwinger quantization approach, quantum mechanics on a Riemannian manifold M with the given action of an intransitive group of isometries is developed. It was shown that quantum mechanics can be determined unequivocally only on submanifolds of M where G acts simply transitively (orbits of G action). The remaining part of the degrees of freedom can be described unequivocally after introducing some additional assumptions. Being logically unmotivated, these assumptions are similar to the canonical quantization postulates. Besides this ambiguity which is of a geometrical nature there is an undetermined gauge field of the order of \(\hbar\) (or higher), vanishing in the classical limit \(\hbar\to 0\).
ISSN:1434-6044
1434-6052
DOI:10.1007/s100520100711