A Numerical Study of Spectral Flows of the Hermitian Wilson-Dirac Operator and the Index Theorem in Abelian Gauge Theories on Finite Lattices

概要

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We investigate numerically the spectrum of the hermitian Wilson-Dirac operator in abelian gauge theories on finite lattices. The spectral flows for a continuous family of abelian gauge fields connecting different topological sectors are shown to have a characteristic structure leading to the lattice index theorem. We find that the index of Neuberger's Dirac operator coincides with the topological charge for a wide class of gauge field configurations. In two dimensions the eigenvalue spectra for some special but nontrivial configurations can be described by a set of characteristic polynomials and the index can be found exactly.
理論物理学刊行会の論文
2002-01-25