The tetrahexahedric Calogero model

authored by

Francisco Correa, Olaf Lechtenfeld

Abstract

We consider the spherical reduction of the rational Calogero model (of type A_n-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.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

External Organisation(s)

Universidad Austral de Chile

Type

Artikel

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

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Strahlung, Atom- und Molekularphysik sowie Optik, Kern- und Hochenergiephysik, Radiologie, Nuklearmedizin und Bildgebung

Electronic version(s)

https://doi.org/10.48550/arXiv.1604.06457 (Access: Offen)
https://doi.org/10.1134/S1547477117020066 (Access: Geschlossen)