Fixed Point Action for the Massless Lattice Schwinger Model *

We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gaussian measure. The resulting action has 123 independent couplings , is bilinear in the Grassmann fields, gauge-invariant by considered the compact gauge transporters and localized within a 7 × 7 lattice centered around one of the fermions. We then simulate the model at various values of β and compare with results obtained with the Wilson fermion action. We find excellent improvement for the studied observables (propagators and masses).