Matter fields in the Lagrangian loop representation: scalar QED

We present the extension of the Lagrangian loop gauge invariant representation in such a way as to include matter fields. The partition function of lattice compact U(1)-Higgs model is expressed as a sum over closed as much as open surfaces. These surfaces correspond to world sheets of loop-like pure electric flux excitations and open electric flux tubes carrying matter fields at their ends. This representation is connected by a duality transformation with the topological representation of the partition function (in terms of world sheets of Nielsen-Olesen strings both closed and open connecting pairs of magnetic monopoles). We have simulated numerically the loop action equivalent to the Villain form of the action and mapped out the β-γ phase diagram of this model. By virtue of the gauge invariance of this description the equilibrium configurations seems to be reached faster than with the ordinary gauge-variant descriptions.