Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory

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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorKress, Jonathan M.
dc.contributor.authorMiller, W., Jr.
dc.date.accessioned2008-10-29T01:09:44Z
dc.date.available2008-10-29T01:09:44Z
dc.date.issued2005-10
dc.description.abstractThis paper is part of a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in real or complex conformally flat spaces. Here we consider classical superintegrable systems with nondegenerate potentials in three dimensions. We show that there exists a standard structure for such systems, based on the algebra of 3×3 symmetric matrices, and that the quadratic algebra always closes at order 6. We show that the spaces of truly second-, third-, fourth-, and sixth-order constants of the motion are of dimension 6, 4, 21, and 56, respectively, and we construct explicit bases for the fourth- and sixth order constants in terms of products of the second order constants.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.citationKalnins, E.G., Kress, J.M. & Miller, W., Jr. (2005). Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory. Journal of Mathematical Physics, 46, 103507.en_US
dc.identifier.doi10.1063/1.2037567en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1177
dc.language.isoen
dc.publisherAmerican Institute of Physicsen_NZ
dc.relation.isPartOfJournal of Mathematical Physicsen_NZ
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/46/103507/1en_US
dc.rightsCopyright 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.jspen_US
dc.subjectMathematicsen_US
dc.subjectmatrix algebraen_US
dc.subjectspace-time configurationsen_US
dc.subjectintegrationen_US
dc.titleSecond order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theoryen_US
dc.typeJournal Articleen_US
pubs.declined2016-05-02T14:11:21.554+1200
pubs.elements-id31937
pubs.issue10en_NZ
pubs.volume46en_NZ
uow.identifier.article-no103507en_NZ
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