The topological characteristics of lattice Dirac operators

Details The topological characteristics of lattice Dirac operators The topological characteristics of lattice Dirac operators

1999-11-08

arxiv.org/abs/hep-lat/9911010v3

Physics

High Energy Physics

High Energy Physics - Lattice

34 pages, LaTeX, 4 eps figures, improved presentation

Scientific paper

We show that even if a lattice Dirac operator satisfies the conditions consisting of locality, free of species doublings, correct continuum behavior, $\gm5$-hermiticity and the Ginsparg-Wilson relation, it does not necessarily have exact zero modes in nontrivial gauge backgrounds. This implies that each lattice Dirac operator has its own topological characteristics which cannot be fixed by these conditions. The role of topological characteristics in the axial anomaly is derived explicitly.

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