TOPOLOGICAL CHARGE AND THE SPECTRUM OF THE FERMION MATRIX IN LATTICE QED(2)

We investigate the interplay between topological charge and the spectr um of the fermion matrix in lattice QED(2) using analytic methods and Monte Carlo simulations with dynamical fermions. A new theorem on the spectral decomposition of the fermion matrix establishes that its real eigenvalues (and corresponding eigenvectors) play a role similar to t he zero eigenvalues (zero-modes) of the Dirac operator in continuous b ackground fields, Using numerical techniques we concentrate on studyin g the real part of the spectrum. These results provide new insights in to the behavior of physical quantities as a function of the topologica l charge, In particular we discuss the fermion determinant, the effect ive action and pseudoscalar densities. (C) 1997 Elsevier Science B.V.