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title:
 
Quantum Integrability of the Dynamics on a Group Manifold
publication:
 
JNMP
volume-issue:   15 - supplement 3
pages:   1 - 12
ISSN:
  1402-9251
DOI:
  doi:10.2991/jnmp.2008.15.s3.1 (how to use a DOI)
author(s):
 
V Aldaya, M Calixto, J Guerrero, F F Lopez-Ruiz
publication date:
 
October 2008
abstract:
 
We study the dynamics of a particle moving on the SU(2) group manifold. An exact quantization of this system is accomplished by finding the unitary and irreducible representations of a finite-dimensional Lie subalgebra of the whole Poisson algebra in phase space. In fact, the basic position and momentum operators, as well as the Hamiltonian, are found in the enveloping algebra of the anti-de Sitter group SO(3,2). The present algorithm mimics the one previously used in Ref. [1]. Our construction can be extended to more general semi-simple Lie groups. This framework would allow us to achieve the quantization of the geodesic motion in a symmetric pseudo-Riemannian manifold.
copyright:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
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