Approximate Ginsparg–Wilson fermions: a first test Original Research Article

We construct a 4-d lattice Dirac operator D using a systematical expansion in terms of simple operators on the lattice. The Ginsparg–Wilson equation turns into a system of coupled equations for the expansion coefficients of D. We solve these equations for a finite parametrization of D and find an approximate solution of the Ginsparg–Wilson equation. We analyze the spectral properties of our D for various ensembles of quenched SU(3) configurations. Improving the gauge field action considerably improves the spectral properties of our D.