  We introduce in a natural and straigthforward way the $loop$ (Lagrangian)
$representation$ for the partition function of pure compact lattice QED. The
corresponding classical lattice loop action is proportional to the quadratic
area of the loop world sheets. We discuss the parallelism between the $loop$
formulation of this model in terms of world sheets of loops and the
$topological$ representation of the Higgs (broken) phase for the non-compact
lattice QED in terms of world sheets of Nielsen-Olesen strings.
