Journal of Nonlinear Mathematical Physics

Volume 15, Issue supplement 3, October 2008, Pages 1 - 12

Quantum Integrability of the Dynamics on a Group Manifold

Authors
V. Aldaya, M. Calixto, J. Guerrero, F.F. Lopez-Ruiz
Corresponding Author
V. Aldaya
Available Online 1 October 2008.
DOI
https://doi.org/10.2991/jnmp.2008.15.s3.1How to use a DOI?
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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
15 - supplement 3
Pages
1 - 12
Publication Date
2008/10
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2008.15.s3.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - V. Aldaya
AU  - M. Calixto
AU  - J. Guerrero
AU  - F.F. Lopez-Ruiz
PY  - 2008
DA  - 2008/10
TI  - Quantum Integrability of the Dynamics on a Group Manifold
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 12
VL  - 15
IS  - supplement 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s3.1
DO  - https://doi.org/10.2991/jnmp.2008.15.s3.1
ID  - Aldaya2008
ER  -