{
  "id": "0707.3772",
  "version": "v1",
  "published": "2007-07-25T15:57:37.000Z",
  "updated": "2007-07-25T15:57:37.000Z",
  "title": "Superintegrability on N-dimensional spaces of constant curvature from so(N+1) and its contractions",
  "authors": [
    "Francisco J. Herranz",
    "Angel Ballesteros"
  ],
  "comment": "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",
  "journal": "Phys.Atom.Nucl.71:905-913,2008",
  "doi": "10.1134/S1063778808050207",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "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).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-25T15:57:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "02.20.Sv",
      "02.40.Ky",
      "02.30.Ik"
    ],
    "keywords": [
      "n-dimensional spaces",
      "constant curvature",
      "superintegrability",
      "arbitrary centrifugal terms",
      "superintegrable hamiltonians"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "journal": "Physics of Atomic Nuclei",
      "year": 2008,
      "month": "May",
      "volume": 71,
      "number": 5,
      "pages": 905
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 757776,
      "adsabs": "2008PAN....71..905H"
    }
  }
}