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

E. G. Kalnins, J. M. Kress, W. Miller

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

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.

Original languageEnglish (US)
Article number053510
JournalJournal of Mathematical Physics
Volume46
Issue number5
DOIs
StatePublished - May 2005

Fingerprint Dive into the research topics of 'Second order superintegrable systems in conformally flat spaces. II. the classical two-dimensional Stäckel transform'. Together they form a unique fingerprint.

Cite this