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

We obtain integral representations for the wave functions of Calogero-type systems, corresponding to the finite-dimensional Lie algebras, using exact evaluation of the 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 the Calogero-Moser model and the models of Calogero-type like the 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 the large-k limit and observe a relation with the Generalized Kontsevich Model.