RELATIVISTIC CALOGERO-MOSER MODEL AS GAUGED WZW THEORY

Integrable deformation of the Calogero-Moser system is examined in the framework of the topological G/G Wess-Zumino-Witten model. It is show n that in the Hamiltonian approach the gauged WZW theory has a Hilbert space, which contains the one of the Ruijsenaars model, The latter ca n be described with the help of Verlinde algebra. Moreover, the evolut ion operator in the quantum mechanical problem has an interpretation i n terms of the path integral in G/G theory with inserted Wilson line, We compute a partition function of the model using techniques from Che m-Simons theory, in particular, some surgeries of simple threefolds,