Quantum Integrability of the Dynamics on a Group Manifold
- 10.2991/jnmp.2008.15.s3.1How to use a DOI?
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. . 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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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 -