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Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform

Abstract
This paper is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. Here we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different spaces. Through the use of this tool we derive and classify for the first time all two-dimensional (2D) superintegrable systems. The underlying spaces are exactly those derived by Koenigs in his remarkable paper giving all 2D manifolds (with zero potential) that admit at least three second order symmetries. Our derivation is very simple and quite distinct. We also show that every superintegrable system is the Stäckel transform of a superintegrable system on a constant curvature space.
Type
Journal Article
Type of thesis
Series
Citation
Kalnins, E.G., Kress, J.M. & Miller, W., Jr. (2005). Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform. Journal of Mathematical Physics, 46, 053510 .
Date
2005-04
Publisher
American Institute of Physics
Degree
Supervisors
Rights
Copyright 2005 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jsp