Topological charge and the spectrum of the fermion matrix in lattice QED2 Original Research Article

We investigate the interplay between topological charge and the spectrum of the fermion matrix in lattice QED2 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 the zero eigenvalues (zero-modes) of the Dirac operator in continuous background fields. Using numerical techniques we concentrate on studying the real part of the spectrum. These results provide new insights into the behavior of physical quantities as a function of the topological charge. In particular we discuss the fermion determinant, the effective action and pseudoscalar densities.