Ginsparg-Wilson relation with R=(a \gamma_5 D)^{2k}

Abstract

The Ginsparg-Wilson relation $D{\gamma }_5+{\gamma }_{5}D=2aDR{\gamma }_{5}D$ with $R=(a{\gamma }_{5}D{)}^{2k}$ 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.

Comments: 4 pages, 1 EPS figure, talk presented at Lattice'00 (Chiral Fermion)