Topological Charge and the Spectrum of the Fermion Matrix in Lattice-QED_2

Details Topological Charge and the Spectrum of the Fermion Matrix in Lattice-QED_2 Topological Charge and the Spectrum of the Fermion Matrix in Lattice-QED_2

1997-07-15

arxiv.org/abs/hep-lat/9707011v2

Nucl.Phys. B508 (1997) 329-352

Physics

High Energy Physics

High Energy Physics - Lattice

33 pages, 10 eps-figures; reference added

Scientific paper

10.1016/S0550-3213(97)00620-2

We investigate the interplay between topological charge and the spectrum 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 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 behaviour of physical quantities as a function of the topological charge. In particular we discuss fermion determinant, effective action and pseudoscalar densities.

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