GAUGE-INVARIANT HAMILTONIAN-FORMULATION OF LATTICE YANG-MILLS THEORY AND THE HEISENBERG DOUBLE

It is known that to get the usual Hamiltonian formulation of lattice Yang-Mills theory in the temporal gauge A(0) = 0 one should place on each link a cotangent bundle of a Lie group. The cotangent bundle may be considered as a limiting case of a so-called Heisenberg double of a Lie group which is one of the basic objects in the theory of Lie-Poisson and quantum groups. It is shown in the paper that there is a generalization of the usual Hamiltonian formulation to the case of the Heisenberg double. The physical phase space of the (1 + 1)-dimensional gamma-deformed Yang-Mills model is proved to be equivalent to the moduli space of flat connections on a two-dimensional torus.