Publications at the Riemann Center
The tetrahexahedric Calogero model
Abstract
We consider the spherical reduction of the rational Calogero model (of type An-1, without the center of mass) as a maximally superintegrable quantum system. It describes a particle on the (n = 2)-sphere in a very special potential. A detailed analysis is provided of the simplest non-separable case, n = 4, whose potential blows up at the edges of a spherical tetrahexahedron, tesselating the two-sphere into 24 identical right isosceles spherical triangles in which the particle is trapped. We construct a complete set of independent conserved charges and of Hamiltonian intertwiners and elucidate their algebra. The key structure is the ring of polynomials in Dunkl-deformed angular momenta, in particular the subspaces invariant and antiinvariant under all Weyl reflections, respectively.
Details
- Organisation(s)
-
Institute of Theoretical Physics
Riemann Center for Geometry and Physics
- External Organisation(s)
-
Universidad Austral de Chile
- Type
- Article
- Journal
- Physics of Particles and Nuclei Letters
- Volume
- 14
- Pages
- 304-311
- No. of pages
- 8
- ISSN
- 1547-4771
- Publication date
- 03.2017
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Radiation, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Radiology Nuclear Medicine and imaging
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.1604.06457 (Access:
Open
)
https://doi.org/10.1134/S1547477117020066 (Access: Closed )
