  It is showed how the Hamiltonian lattice $loop$ $representation$ can be cast
straightforwardly in the Lagrangian formalism. The procedure is general and
here we present the simplest case: pure compact QED. This connection has been
shaded by the non canonical character of the algebra of the fundamental loop
operators. The loops represent tubes of electric flux and can be considered the
dual objects to the Nielsen-Olesen strings supported by the Higgs broken phase.
The lattice loop classical action corresponding to the Villain form is
proportional to the quadratic area of the loop world sheets and thus it is
similar to the Nambu string action. This loop action is used in a Monte Carlo
simulation and its appealing features are discussed.
