Details
| Original language | English |
|---|---|
| Article number | 162 |
| Journal | Journal of high energy physics |
| Volume | 2013 |
| Issue number | 7 |
| Publication status | Published - 2013 |
Abstract
The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of ℝn to the 'angular Calogero-Moser model' on the sphere S n-1.We discuss the energy spectrum of this quantum system, its degeneracies and the eigenstates. The spectral flow with the coupling parameter yields isospectrality for integer increments. Decoupling the center of mass before effecting the spherical reduction produces a 'relative angular Calogero-Moser model', which is analyzed in parallel. We generalize our considerations to the Calogero-Moser models associated with Coxeter groups. Finally, we attach spin degrees of freedom to our particles and extend the results to the spin-Calogero system.
Keywords
- Integrable Equations in Physics, Integrable Field Theories
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Journal of high energy physics, Vol. 2013, No. 7, 162, 2013.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The quantum angular Calogero-Moser model
AU - Feigin, Mikhail
AU - Lechtenfeld, Olaf
AU - Polychronakos, Alexios P.
N1 - Copyright: Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013
Y1 - 2013
N2 - The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of ℝn to the 'angular Calogero-Moser model' on the sphere S n-1.We discuss the energy spectrum of this quantum system, its degeneracies and the eigenstates. The spectral flow with the coupling parameter yields isospectrality for integer increments. Decoupling the center of mass before effecting the spherical reduction produces a 'relative angular Calogero-Moser model', which is analyzed in parallel. We generalize our considerations to the Calogero-Moser models associated with Coxeter groups. Finally, we attach spin degrees of freedom to our particles and extend the results to the spin-Calogero system.
AB - The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of ℝn to the 'angular Calogero-Moser model' on the sphere S n-1.We discuss the energy spectrum of this quantum system, its degeneracies and the eigenstates. The spectral flow with the coupling parameter yields isospectrality for integer increments. Decoupling the center of mass before effecting the spherical reduction produces a 'relative angular Calogero-Moser model', which is analyzed in parallel. We generalize our considerations to the Calogero-Moser models associated with Coxeter groups. Finally, we attach spin degrees of freedom to our particles and extend the results to the spin-Calogero system.
KW - Integrable Equations in Physics
KW - Integrable Field Theories
UR - http://www.scopus.com/inward/record.url?scp=84881420846&partnerID=8YFLogxK
U2 - 10.1007/JHEP07(2013)162
DO - 10.1007/JHEP07(2013)162
M3 - Article
AN - SCOPUS:84881420846
VL - 2013
JO - Journal of high energy physics
JF - Journal of high energy physics
SN - 1126-6708
IS - 7
M1 - 162
ER -