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

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