{
  "id": "0812.1882",
  "version": "v1",
  "published": "2008-12-10T10:33:22.000Z",
  "updated": "2008-12-10T10:33:22.000Z",
  "title": "Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles",
  "authors": [
    "Angel Ballesteros",
    "Alberto Enciso",
    "Francisco J. Herranz",
    "Orlando Ragnisco"
  ],
  "comment": "22 pages",
  "journal": "Annals Phys.324:1219-1233,2009",
  "doi": "10.1016/j.aop.2009.03.001",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "The N-dimensional Hamiltonian H formed by a curved kinetic term (depending on a function f), a central potential (depending on a function U), a Dirac monopole term, and N centrifugal terms is shown to be quasi-maximally superintegrable for any choice of the functions f and U. This result is proven by making use of the underlying sl(2,R)-coalgebra symmetry of H in order to obtain a set of (2N-3) functionally independent integrals of the motion, that are explicitly given. Such constants of the motion are \"universal\" since all of them are independent of both f and U. This Hamiltonian describes the motion of a particle on any ND spherically symmetric curved space (whose metric is specified by a function f) under the action of an arbitrary central potental U, and includes simultaneously a monopole-type contribution together with N centrifugal terms that break the spherical symmetry. Moreover, we show that two appropriate choices for U provide the \"intrinsic\" oscillator and the KC potentials on these curved manifolds. As a byproduct, the MIC-Kepler, the Taub-NUT and the so called multifold Kepler systems are shown to belong to this class of superintegrable Hamiltonians, and new generalizations thereof are obtained. The Kepler and oscillator potentials on N-dimensional generalizations of the four Darboux surfaces are discussed as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-10T10:33:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "02.40.Ky",
      "02.30.Ik"
    ],
    "keywords": [
      "centrifugal terms",
      "n-dimensional curved spaces",
      "central potential",
      "superintegrability",
      "hamiltonian"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Annals of Physics",
      "year": 2009,
      "month": "Jun",
      "volume": 324,
      "number": 6,
      "pages": 1219
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 805363,
      "adsabs": "2009AnPhy.324.1219B"
    }
  }
}