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Geometric quantization of the momentum mapping associated with coupled harmonic oscillators

Abstract

Here we study a mechanical system whose dynamics is governed by a pair of commuting Hamiltonians which can be considered as the components of the momentum mapping associated with a torus action. We reduce the system via this momentum map and apply the geometric quantization scheme to its orbit manifold. In this way we obtain the energy levels along with the corresponding multiplicities. Finally, we point out that our considerations can be easily generalized giving in this way a new insight into the theory of representations of Lie groups in terms of Hamiltonian Mechanics. (author). 8 refs.
Authors:
Mladenov, I M; [1]  Tsanov, V V [2] 
  1. International Centre for Theoretical Physics, Trieste (Italy)
  2. Sofia Univ., Sofia (Bulgaria). Dept. of Mathematics
Publication Date:
May 01, 1991
Product Type:
Technical Report
Report Number:
IC-91/42
Reference Number:
SCA: 661100; PA: AIX-23:028606; SN: 92000699594
Resource Relation:
Other Information: PBD: May 1991
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HARMONIC OSCILLATORS; QUANTIZATION; CLASSICAL MECHANICS; ENERGY LEVELS; HAMILTONIANS; LIE GROUPS; MATHEMATICAL MANIFOLDS; PHASE SPACE; QUANTUM MECHANICS; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10132850
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE92622381; TRN: XA9230787028606
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
10 p.
Announcement Date:
Jul 04, 2005

Citation Formats

Mladenov, I M, and Tsanov, V V. Geometric quantization of the momentum mapping associated with coupled harmonic oscillators. IAEA: N. p., 1991. Web.
Mladenov, I M, & Tsanov, V V. Geometric quantization of the momentum mapping associated with coupled harmonic oscillators. IAEA.
Mladenov, I M, and Tsanov, V V. 1991. "Geometric quantization of the momentum mapping associated with coupled harmonic oscillators." IAEA.
@misc{etde_10132850,
title = {Geometric quantization of the momentum mapping associated with coupled harmonic oscillators}
author = {Mladenov, I M, and Tsanov, V V}
abstractNote = {Here we study a mechanical system whose dynamics is governed by a pair of commuting Hamiltonians which can be considered as the components of the momentum mapping associated with a torus action. We reduce the system via this momentum map and apply the geometric quantization scheme to its orbit manifold. In this way we obtain the energy levels along with the corresponding multiplicities. Finally, we point out that our considerations can be easily generalized giving in this way a new insight into the theory of representations of Lie groups in terms of Hamiltonian Mechanics. (author). 8 refs.}
place = {IAEA}
year = {1991}
month = {May}
}