LATTICE SCHWINGER MODEL WITH INTERPOLATED GAUGE-FIELDS

We analyze the Schwinger model on an infinite lattice using the contin uum definition of the fermion determinant and a linear interpolation o f the lattice gauge fields. The possible class of interpolations for t he gauge fields, compatible with gauge invariance, is discussed. The e ffective action for the lattice gauge field is computed for the Wilson formulation as well as for noncompact lattice gauge fields. For the n oncompact formulation we prove that the model has a critical point wit h diverging correlation length at zero gauge coupling e. We compute th e chiral condensate for e>0 and compare the result to the N-flavor con tinuum Schwinger model. This indicates that there is only one flavor o f fermions with the same chiral properties as in the continuum model, already before the continuum limit is performed. We discuss how operat ors have to be renormalized in the continuum limit to obtain the conti nuum Schwinger model.