QUANTUM INTEGRABLE SYSTEMS OF PARTICLES AS GAUGE-THEORIES

We study quantum integrable systems of interacting particles from the point of view proposed by A. Gorsky and N. Nekrasov. We obtain the Sut herland system by a Hamiltonian reduction of an integrable system on t he cotangent bundles to an affine su(N) algebra and show that it coinc ides with the Yang-Mills theory on a cylinder. We point out that there exists a tower of 2d quantum,field theories. The top of this tower is the gauged G/G WZW model on a cylinder with an inserted Wilson line i n an appropriate representation, which in our approach corresponds to Ruijsenaars' relativistic Calogero model. Its degeneration yields the 2d Yang-Mills theory, whose small radius limit is the Calogero model i tself. We make some comments about the spectra and eigenstates of the models, which one can get from their equivalence with the field theori es. Also we point out some possibilities of elliptic deformations of t hese constructions.