Quantum Integrability of the Dynamics on a Group Manifold

DOI

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.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - V. Aldaya
AU  - M. Calixto
AU  - J. Guerrero
AU  - F.F. Lopez-Ruiz
PY  - 2008
DA  - 2008/10/01
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  - 10.2991/jnmp.2008.15.s3.1
ID  - Aldaya2008
ER  -