Generalized Calogero model in arbitrary dimensions

Details Generalized Calogero model in arbitrary dimensions Generalized Calogero model in arbitrary dimensions

2004-05-14

arxiv.org/abs/hep-th/0405131v1

Phys.Lett. B594 (2004) 241-246

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, no figures, to be published in Phys.Lett.B

Scientific paper

10.1016/j.physletb.2004.05.034

We define a new multispecies model of Calogero type in D dimensions with harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we indicate how to find the complete set of the states in Bargmann-Fock space. There are towers of states, with equidistant energy spectra in each tower. We explicitely construct all polynomial eigenstates, namely the center-of-mass states and global dilatation modes, and find their corresponding eigenenergies. We also construct ladder operators for these global collective states. Analysing corresponding Fock space, we detect the universal critical point at which the model exhibits singular behavior. The above results are universal for all systems with underlying conformal SU(1,1) symmetry.

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