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arXiv · 1508.04925

The tetrahexahedric angular Calogero model

Francisco Correa·Olaf Lechtenfeld
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Abstract

The spherical reduction of the rational Calogero model (of type $A_{n-1}$ and after removing the center of mass) is considered as a maximally superintegrable quantum system, which describes a particle on the $(n{-}2)$-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.

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Francisco Correa, Olaf Lechtenfeld. 2015-11-05. The tetrahexahedric angular Calogero model. https://arxiv.org/abs/1508.04925

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