PATH-INTEGRAL FOR THE LOOP REPRESENTATION OF LATTICE GAUGE-THEORIES

We show how the Hamiltonian lattice loop representation can be cast st raightforwardly in the path integral formalism. The procedure is gener al for any gauge theory. Here we present in detail the simplest case: pure compact QED. The lattice loop path integral approach allows us to knit together the power of statistical algorithms with the transparen cy of the gauge-invariant loop description. The results produced by nu merical simulations with the loop classical action for different latti ce models are discussed. We also analyze the lattice path integral in terms of loops for the non-Abelian theory.