  We show how the Hamiltonian lattice loop representation can be cast
straightforwardly in the path integral formalism. The procedure is general for
any gauge theory. Here we present in detail the simplest case: pure compact
QED. We also analyze the non-Abelian Yang-Mills theory. The lattice loop path
integral approach allows to knit together the power of statistical algorithms
with the transparency of the gauge invariant loop description. The results
produced by numerical simulations with the loop classical action for different
lattice models are discused.
