Research Commons
      • Browse 
        • Communities & Collections
        • Titles
        • Authors
        • By Issue Date
        • Subjects
        • Types
        • Series
      • Help 
        • About
        • Collection Policy
        • OA Mandate Guidelines
        • Guidelines FAQ
        • Contact Us
      • My Account 
        • Sign In
        • Register
      View Item 
      •   Research Commons
      • University of Waikato Research
      • Computing and Mathematical Sciences
      • Computing and Mathematical Sciences Papers
      • View Item
      •   Research Commons
      • University of Waikato Research
      • Computing and Mathematical Sciences
      • Computing and Mathematical Sciences Papers
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

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

      Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr.
      Thumbnail
      Files
      Kalnins second-order superintegrable systems.pdf
      228.0Kb
      DOI
       10.1063/1.2037567
      Link
       link.aip.org
      Find in your library  
      Citation
      Export citation
      Kalnins, 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.
      Permanent Research Commons link: https://hdl.handle.net/10289/1177
      Abstract
      This 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.
      Date
      2005-10
      Type
      Journal Article
      Publisher
      American Institute of Physics
      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
      Collections
      • Computing and Mathematical Sciences Papers [1455]
      Show full item record  

      Usage

      Downloads, last 12 months
      80
       
       
       

      Usage Statistics

      For this itemFor all of Research Commons

      The University of Waikato - Te Whare Wānanga o WaikatoFeedback and RequestsCopyright and Legal Statement