Ginsparg-Wilson relation with R=(a γ_5 D)^{2k}

Abstract

The Ginsparg-Wilson relation $D γ_5 + γ_5 D = 2 a D R γ_5 D$ with $R = (a γ_5 D)^{2k}$ is discussed. An explicit realization of D is constructed. It is shown that this sequence of topologically-proper lattice Dirac operators tend to a nonlocal operator in the limit $k \to \infty$. This suggests that the locality of a lattice Dirac operator is irrelevant to its index.