The scaling of exact and approximate Ginsparg-Wilson fermions

We construct a number of lattice fermions, which fulfill the Ginsparg-Wilso n relation either exactly or approximately, and test them in the framework of the 2-flavor Schwinger model. We start from explicit approximations with in a short range, and study this formulation, as well as its correction to an exact Ginsparg-Wilson fermion by the "overlap formula". Then we suggest a new method to realize this correction perturbatively, without using the t edious square root operator. In this way we combine many favorable properti es: good chiral behavior, small mass renormalization, excellent scaling and rotational invariance, as well as a relatively modest computational effort , which makes such formulations most attractive for QCD. (C) 2000 Elsevier Science B.V. All rights reserved.