Superintegrability on N-dimensional spaces of constant curvature from so(N+1) and its contractions
| dc.creator | Herranz, Francisco J. | |
| dc.creator | Ballesteros, Angel | |
| dc.date | 2007-07-25 | |
| dc.date.accessioned | 2026-07-07T11:41:36Z | |
| dc.date.available | 2026-07-07T11:41:36Z | |
| dc.description | The Lie-Poisson algebra so(N+1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the ND spherical, Euclidean, hyperbolic, Minkowskian and (anti-)de Sitter spaces. We firstly present a Hamiltonian which is a superposition of an arbitrary central potential with N arbitrary centrifugal terms. Such a system is quasi-maximally superintegrable since this is endowed with 2N-3 functionally independent constants of the motion (plus the Hamiltonian). Secondly, we identify two maximally superintegrable Hamiltonians by choosing a specific central potential and finding at the same time the remaining integral. The former is the generalization of the Smorodinsky-Winternitz system to the above six spaces, while the latter is a generalization of the Kepler-Coulomb potential, for which the Laplace-Runge-Lenz N-vector is also given. All the systems and constants of the motion are explicitly expressed in a unified form in terms of ambient and polar coordinates as they are parametrized by two contraction parameters (curvature and signature of the metric). | |
| dc.description | 14 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 | |
| dc.identifier | https://arxiv.org/abs/0707.3772 | |
| dc.identifier | http://arxiv.org/abs/0707.3772 | |
| dc.identifier | Phys.Atom.Nucl.71:905-913,2008 | |
| dc.identifier | doi:10.1134/S1063778808050207 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/200593 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Superintegrability on N-dimensional spaces of constant curvature from so(N+1) and its contractions | |
| dc.type | text |