Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature

Details Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature

2006-11-16

arxiv.org/abs/math-ph/0611040v3

SIGMA 3 (2007), 026, 20 pages

Physics

Mathematical Physics

This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (

Scientific paper

10.3842/SIGMA.2007.026

An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden non-standard quantum sl(2,R) Poisson coalgebra symmetry. As a concrete application, one of this Hamiltonians is shown to generate the geodesic motion on certain manifolds with a non-constant curvature that turns out to be a function of the deformation parameter z. Moreover, another Hamiltonian in this family is shown to generate geodesic motions on Riemannian and relativistic spaces all of whose sectional curvatures are constant and equal to the deformation parameter z. This approach can be generalized to arbitrary dimension by making use of coalgebra symmetry.

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