Superintegrability on sl(2)-coalgebra spaces
Abstract
We review a recently introduced set of N-dimensional quasi-maximally superintegrable Hamiltonian systems describing geodesic motions, that can be used to generate "dynamically" a large family of curved spaces. From an algebraic viewpoint, such spaces are obtained through kinetic energy Hamiltonians defined on either the sl(2) Poisson coalgebra or a quantum deformation of it. Certain potentials on these spaces and endowed with the same underlying coalgebra symmetry have been also introduced in such a way that the superintegrability properties of the full system are preserved. Several new N=2 examples of this construction are explicitly given, and specific Hamiltonians leading to spaces of non-constant curvature are emphasized.
Cite
@article{arxiv.0707.3769,
title = {Superintegrability on sl(2)-coalgebra spaces},
author = {Angel Ballesteros and Francisco J. Herranz and Orlando Ragnisco},
journal= {arXiv preprint arXiv:0707.3769},
year = {2008}
}
Comments
12 pages. Based on the contribution presented at the "XII International Conference on Symmetry Methods in Physics", Yerevan (Armenia), July 2006. To appear in Physics of Atomic Nuclei