HAMILTONIAN-SYSTEMS OF CALOGERO-TYPE, AND 2-DIMENSIONAL YANG-MILLS THEORY

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