A new integrable system on the sphere and conformally equivariant quantization

Details A new integrable system on the sphere and conformally equivariant quantization A new integrable system on the sphere and conformally equivariant quantization

2010-07-16

arxiv.org/abs/1007.2755v2

Journal of Geometry and Physics 61, 1 (2011) 1329-1347

Physics

Mathematical Physics

LaTeX, 33 pages. Minor corrections. Published version

Scientific paper

10.1016/j.geomphys.2011.02.020

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) St\"ackel 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.

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