Some remarks on the Ginsparg–Wilson fermion Original Research Article

We note that Fujikawaʹs proposal of generalization of the Ginsparg–Wilson relation is equivalent to setting R=(aγ5D)2k in the original Ginsparg–Wilson relation Dγ5+γ5D=2aDRγ5D . An explicit realization of D follows from the Overlap construction. The general properties of D are derived. The chiral properties of these higher-order ( k>0 ) realizations of Overlap Dirac operator are compared to those of the Neuberger–Dirac operator ( k=0 ), in terms of the fermion propagator, the axial anomaly and the fermion determinant in a background gauge field. Our present results (up to lattice size 16×16 ) indicate that the chiral properties of the Neuberger–Dirac operator are better than those of higher-order ones.