Gauge invariant Hamiltonian formulation of lattice Yang-Mills theory

Abstract

It it known that to get the usual Hamiltonian formulation of lattice Yang-Mills theory in the temporal gauge A0 = 0 one should place on every link the 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 .