Quantum mechanics on Riemannian manifold in Schwinger's quantization approach II |
| |
Authors: | NM Chepilko AV Romanenko |
| |
Institution: | (1) Physics Institute of the Ukrainian Academy of Sciences, Kyiv-03 028, Ukraine , UA;(2) Kyiv Taras Shevchenko University, Department of Physics, Kyiv-03 022, Ukraine , UA |
| |
Abstract: | 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.
Received: 27 June 2000 / Revised version: 10 May 2001 / Published online: 19 July 2001 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|