The tetrahexahedric angular Calogero model

2015, October 28
Francisco Correa and Olaf Lechtenfeld
JHEP 1510 (2015)

The spherical reduction of the rational Calogero model (of type A_{n1} and after removing the center of mass) is considered as a maximally superintegrable quantum system, which describes a particle on the (n2)-sphere subject to a very particular potential. We present a detailed analysis of the simplest non-separable case, n=4, whose potential is singular at the edges of a spherical tetrahexahedron. A complete set of independent conserved charges and of Hamiltonian intertwiners is constructed, and their algebra is elucidated. They arise from the ring of polynomials in Dunkl-deformed angular momenta, by classifying the subspaces invariant and antiinvariant under all Weyl reflections, respectively.