The scaling of exact and approximate Ginsparg–Wilson fermions Original Research Article

We construct a number of lattice fermions, which fulfill the Ginsparg–Wilson relation either exactly or approximately, and test them in the framework of the 2-flavor Schwinger model. We start from explicit approximations within 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 tedious square root operator. In this way we combine many favorable properties: 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.