The lattice Schwinger model as a discrete sum of filled Wilson loops

Using techniques from hopping expansion we identically map the lattice Schw inger model with Wilson fermions to a model of oriented loops on the lattic e. This is done by first computing the explicit form of the fermion determi nant in the external field. Subsequent integration of the gauge fields rend ers a sum over all loop configurations with simple Gaussian weights dependi ng on the number of plaquettes enclosed by the loops. In our new representa tion vacuum expectation values of local fermionic operators (scalars, vecto rs) can be computed by simply counting the loop flow through the sites (lin ks) supporting the scalars (vectors). The strong coupling limit, possible a pplications of our methods to 4-D models and the introduction of a chemical potential are discussed. (C) 1999 Elsevier Science B.V. All rights reserve d.