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      Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics

      Kalnins, Ernie G.; Miller, W., Jr.; Post, Sarah
      DOI
       10.1088/1751-8113/43/3/035202
      Link
       iopscience.iop.org
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      Citation
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      Kalnins, E.G., Miller, W. Jr. & Post, S. (2010). Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics. Journal of Physics A: Mathematical and Theoretical, 43(3), 035202.
      Permanent Research Commons link: https://hdl.handle.net/10289/4754
      Abstract
      We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the momenta to polynomials in the momenta. We study specializations of these actions which preserve polynomials and also the structure of the symmetry algebras in both the classical and quantum cases. We give several examples of non-constant curvature third- and fourth-order superintegrable systems in two space dimensions obtained via CCM, with some details on the structure of the symmetry algebras preserved by the transform action.
      Date
      2010
      Type
      Journal Article
      Publisher
      IOP Publishing
      Collections
      • Computing and Mathematical Sciences Papers [1455]
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