Eur. Phys. J. C 21, 757-767 (2001)
DOI: 10.1007/s100520100711
Quantum mechanics on Riemannian manifold in Schwinger's quantization approach III
N.M. Chepilko1 and A.V. Romanenko21 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: 19 February 2001 / Revised version: 10 May 2001 / Published online: 6 July 2001 -© Springer-Verlag / Società Italiana di Fisica 2001 )
Abstract
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 (or higher), vanishing in the
classical limit
.
© Società Italiana di Fisica, Springer-Verlag 2001