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Quadrics on complex Riemannian spaces of constant curvature, separation of variables, and the Gaudin magnet

J. Math. Phys. 35, 1710 (1994); doi:10.1063/1.530566

Issue Date: April 1994

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E. G. Kalnins, V. B. Kuznetsov, and Willard Miller, Jr.
Department of Mathematics and Statistics, University of Waikato, Hamilton, New Zealand
Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
School of Mathematics and Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, Minnesota 55455
Integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature are considered herein. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of the authors, extends to coordinates of this type. The complete classification of these separable coordinate systems is provided by means of the corresponding L matrices for the Gaudin magnet. The limiting procedures (or epsilon calculus) which relate various degenerate orthogonal coordinate systems play a crucial role in the classification of all such systems. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
History: Received 2 August 1993; accepted 23 November 1993
Permalink: http://link.aip.org/link/?JMAPAQ/35/1710/1
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KEYWORDS and PACS

Keywords
PACS
  • 02.20.-a
    Mathematical methods in physics Group theory
  • 02.40.-k
    Mathematical methods in physics Geometry, differential geometry, and topology
  • 02.90.+p
    Mathematical methods in physics Other topics in mathematical methods in physics
  • 03.65.Fd
    Classical and quantum physics: mechanics and fields Quantum mechanics Algebraic methods
  • YEAR: 1994

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ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (21)
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  21. E. G. Kalnins and W. Miller, Jr., “Intrinsic characterization of orthogonal separation of one coordinate in the Hamilton-Jacobi equation,” J. Phys. A 15, 2003 (1982).

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