Aspects of generalized Calogero model

Abstract

A multispecies model of Calogero type in $D\ge 1$ dimensions is constructed. The model includes harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we find the exact eigenenergies corresponding to a class of the exact global collective states. Analysing corresponding Fock space, we detect the universal critical point at which the model exhibits singular behaviour.

7 pages, presented at XIII International Colloquium "Integrable Systems and Quantum Groups", June 17-19 2004.,Prague