PHYSICAL PHASE-SPACE OF THE LATTICE YANG-MILLS THEORY AND THE MODULI SPACE OF FLAT CONNECTIONS ON A RIEMANN SURFACE

It is shown that the physical phase space of the gamma-deformed Hamilt onian lattice in the Yang-Mills theory coincides as a Poisson manifold with the moduli space of hat connections on a Riemann surface with L - V + 1 handles and, therefore, with the physical phase space of the c orresponding (2 + 1)-dimensional Chern-Simons model. Here, L and V are , respectively, the total number of links and vertices of the lattice. The deformation parameter gamma is identified with 2 pi/k, where k is an integer appearing in the Chern-Simons action.