A physical interpretation of the eigenmodes of the Ginsparg-Wilson type Dirac operator

Abstract

Based on Ginsparg and Wilsons' block spin approach in the derivation of the Ginsparg-Wilson relation, we study the correspondence of the eigenmodes of the Dirac operators in the continuum and lattice theories. After introducing a suitable cut-off in the continuum theory, we identify unphysical modes of the lattice Dirac operator which do not correspond to any physical modes of the regularized continuum Diract operator. We also show that the zero modes of the Dirac operator in the continuum theory are transformed to the zero modes of the Dirac operator on the lattice.