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

Abstract

We study characteristic features of the eigenvalues of the Wilson-Dirac operator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. In particular we discuss the role of eigenvectors with real eigenvalues as the lattice equivalents of the continuum zero-modes. We demonstrate, that those properties of the spectrum which correspond to non-trivial topology are stable under adding fluctuations to the gauge fields. The behavior of the spectrum in a fully quantized theory is discussed using QED_2 as an example.