Superintegrability on N-dimensional spaces of constant curvature from so(N+1) and its contractions

dc.creatorHerranz, Francisco J.
dc.creatorBallesteros, Angel
dc.date2007-07-25
dc.date.accessioned2026-07-07T11:41:36Z
dc.date.available2026-07-07T11:41:36Z
dc.descriptionThe 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.description14 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.identifierhttps://arxiv.org/abs/0707.3772
dc.identifierhttp://arxiv.org/abs/0707.3772
dc.identifierPhys.Atom.Nucl.71:905-913,2008
dc.identifierdoi:10.1134/S1063778808050207
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/200593
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleSuperintegrability on N-dimensional spaces of constant curvature from so(N+1) and its contractions
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