Details
| Original language | English |
|---|---|
| Pages (from-to) | 304-311 |
| Number of pages | 8 |
| Journal | Physics of Particles and Nuclei Letters |
| Volume | 14 |
| Issue number | 2 |
| Publication status | Published - Mar 2017 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Radiation
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Medicine(all)
- Radiology Nuclear Medicine and imaging
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In: Physics of Particles and Nuclei Letters, Vol. 14, No. 2, 03.2017, p. 304-311.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The tetrahexahedric Calogero model
AU - Correa, Francisco
AU - Lechtenfeld, Olaf
N1 - Funding information: He is partially supported by the NSF grant DMS 9971282 and Alexander von Humboldt Foundation. ‡ His research is partially supported by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. Publication 774. *
PY - 2017/3
Y1 - 2017/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85015422648&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1604.06457
DO - 10.48550/arXiv.1604.06457
M3 - Article
AN - SCOPUS:85015422648
VL - 14
SP - 304
EP - 311
JO - Physics of Particles and Nuclei Letters
JF - Physics of Particles and Nuclei Letters
SN - 1547-4771
IS - 2
ER -