Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory

Abstract

We obtain integral representations for the wave functions of Calogero-type systems,corresponding to the finite-dimentional Lie algebras,using exact evaluation of path integral.We generalize these systems to the case of the Kac-Moody algebras and observe the connection of them with the two dimensional Yang-Mills theory.We point out that Calogero-Moser model and the models of Calogero type like Sutherland one can be obtained either classically by some reduction from two dimensional Yang-Mills theory with appropriate sources or even at quantum level by taking some scaling limit.We investigate large k limit and observe a relation with Generalized Kontsevich Model.