E G Kalnins et al 2010 J. Phys. A: Math. Theor. 43 035202 doi:10.1088/1751-8113/43/3/035202
Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics
E G Kalnins1, W Miller Jr2 and S Post2
Show affiliationsWe 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.
- PACS
- MSC
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81S30 Phase space methods including Wigner distributions, etc.
81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
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Issue 3 (22 January 2010)
Received 26 August 2009, in final form 17 November 2009
Published 17 December 2009
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Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics
E G Kalnins et al 2010 J. Phys. A: Math. Theor. 43 035202
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