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hal-00502566, version 1

A new integrable system on the sphere and conformally equivariant quantization

Christian Duval () 1, Galliano Valent () 2

(2010-07-15)

Abstract: Taking full advantage of two independent projectively equivalent metrics on the ellipsoid leading to Liouville integrability of the geodesic flow via the well-known Jacobi-Moser system, we disclose a novel integrable system on the sphere $S^n$, namely the ``dual Moser'' system. The latter falls, along with the Jacobi-Moser and Neumann-Uhlenbeck systems, into the category of (locally) Stäckel systems. Moreover, it is proved that quantum integrability of both Neumann-Uhlenbeck and dual Moser systems is insured by means of the conformally equivariant quantization procedure.

  • 1:  Centre de Physique Théorique (CPT)
  • CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var
  • 2:  Laboratoire de Physique Théorique et Hautes Energies (LPTHE)
  • CNRS : UMR7589 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
  • Domain : Physics/Mathematical Physics
    Mathematics/Mathematical Physics
    Nonlinear Sciences/Exactly Solvable and Integrable Systems
  • Keywords : Classical integrability – Projectively equivalent metrics – Stäckel systems – Conformally equivariant quantization – Quantum integrability
  • Available versions :  v1 (2010-07-16) v2 (2011-05-31)
 
  • hal-00502566, version 1
  • http://hal.archives-ouvertes.fr/hal-00502566
  • oai:hal.archives-ouvertes.fr:hal-00502566
  • From: Christian Duval <>
  • Submitted on: Thursday, 15 July 2010 11:56:01
  • Updated on: Friday, 16 July 2010 14:32:50