On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations

We study characteristic features of the eigenvalues of the Wilson-Dirac ope rator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. In particular we discuss the role o f eigenvectors with real eigenvalues as the lattice equivalents of the cont inuum zero-modes. We demonstrate that those properties of the spectrum whic h correspond to non-trivial topology are stable under adding fluctuations t o the gauge fields, The behavior of the spectrum in a fully quantized theor y is discussed using QED(2) as an example. (C) 1999 Published by Elsevier S cience B.V.