Generalized Calogero model in arbitrary dimensions

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

Matrix oscillator and Calogero-type models

We study a single matrix oscillator with the quadratic Hamiltonian and deformed commutation relations. It is equivalent to the multispecies Calogero model in one dimension, with inverse-square two-body and three-body interactions. Specially, we have constructed a new matrix realization of the Calogero model for identical particles, without using exchange operators. The critical points at which singular behaviour occurs are briefly discussed.Comment: Accepted for publication in Phys.Lett.