The quantum angular Calogero-Moser model

authored by

Mikhail Feigin, Olaf Lechtenfeld, Alexios P. Polychronakos

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 ℝ_n 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.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

External Organisation(s)

University of Glasgow
New York University
City University of New York

Type

Artikel

Journal

Journal of high energy physics

Volume

2013

ISSN

1126-6708

Publication date

2013

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.1007/JHEP07(2013)162 (Access: Unbekannt)