Approximate Ginsparg-Wilson Fermions for QCD

Lattice fermions obeying the Ginsparg-Wilson relation do correctly represent the physical properties related to chirality. This can be achieved by local fermions, which involve an infinite number of couplings, however. For practical purposes, it is useful to first construct approximate Ginsparg-Wilson fermions within a short range. We report on a successful construction in QCD at β = 6. The good quality of the approximation is observed from the spectrum, which is situated close to a Ginsparg-Wilson circle. These fermions also provide an excellent approximation to rotational symmetry and they are promising for a good scaling, since they arise from the perfect action framework. Their insertion into the overlap formula renders the Ginsparg-Wilson relation exact. It leads to an improved overlap fermion with a high level of locality. This insertion is statistically on safe grounds at β ≳ 5.6.