Lattice Fermions Coupled to Interpolated Gauge Fields - Results in 2 Dimensions

We discuss a new approach for putting gauge theories on the lattice. The gauge fields are defined on the lattice only, but are interpolated to the interior of the lattice cells, where they couple to continuum fermions. The purpose of this approach is to avoid doublers and keep the chiral symmetry of the action intact. In two dimensional models (Schwinger model and chiral Schwinger model) many results for this hybrid approach can be obtained analytically. For the vectorlike Schwinger model we concentrate on proving the existence of a critical point where the continuum limit can be constructed, on analyzing the chiral properties and on proving the Osterwalder-Schrader positivity which allows the reconstruction of the physical Hilbert space. We conclude with outlining how the results can be generalized to the chiral Schwinger model.