  Using techniques from hopping expansion we identically map the lattice
Schwinger model with Wilson fermions to a model of oriented loops on the
lattice. This is done by first computing the explicit form of the fermion
determinant in the external field. Subsequent integration of the gauge fields
renders a sum over all loop configurations with simple Gaussian weights
depending on the number of plaquettes enclosed by the loops. In our new
representation vacuum expectation values of local fermionic operators (scalars,
vectors) can be computed by simply counting the loop flow through the sites
(links) supporting the scalars (vectors). The strong coupling limit, possible
applications of our methods to 4-D models and the introduction of a chemical
potential are discussed.
