A new integrable system on the sphere and conformally equivariant quantization

作者：Duval C^*; Valent G

来源：Journal of Geometry and Physics, 2011, 61(8): 1329-1347.

DOI：10.1016/j.geomphys.2011.02.020

• Classical integrability
• Projectively equivalent metrics
• Stackel systems
• Conformally equivariant quantization
• Quantum integrability

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) Stackel systems. Moreover, it is proved that quantum integrability of both Neumann-Uhlenbeck and dual Moser systems is ensured by means of the conformally equivariant quantization procedure.

• 出版日期2011-8