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

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.
Type
Journal Article
Type of thesis
Series
Citation
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.
Date
2010
Publisher
IOP Publishing
Degree
Supervisors
Rights