The quantum angular Calogero-Moser model
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 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.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- July 2013
- DOI:
- 10.1007/JHEP07(2013)162
- arXiv:
- arXiv:1305.5841
- Bibcode:
- 2013JHEP...07..162F
- Keywords:
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- Integrable Equations in Physics;
- Integrable Field Theories;
- Mathematical Physics;
- High Energy Physics - Theory;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 1+19 pages, v2: minor corrections, 4 refs. added, version published in JHEP