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      Superintegrability in a non-conformally-flat space

      Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr.
      DOI
       10.1088/1751-8113/46/2/022002
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      Kalnins, E. G., Kress, J. M., & Miller, W. (2013). Superintegrability in a non-conformally-flat space. Journal of Physics A: Mathematical and Theoretical, 46(2), 022002.
      Permanent Research Commons link: https://hdl.handle.net/10289/7158
      Abstract
      Superintegrable systems in two- and three-dimensional spaces of constant curvature have been extensively studied. From these, superintegrable systems in conformally flat spaces can be constructed by Stackel transform. In this paper a method developed to establish the superintegrability of the Tremblay-Turbiner-Winternitz system in two dimensions is extended to higher dimensions and a superintegrable system on a non-conformally-flat four-dimensional space is found. In doing so, curvature corrections to the corresponding classical potential are found to be necessary. It is found that some subalgebras of the symmetry algebra close polynomially.
      Date
      2013
      Type
      Journal Article
      Publisher
      Institute of Physics
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      • Computing and Mathematical Sciences Papers [1455]
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