Dirac operator index and topology of lattice gauge fields

Details Dirac operator index and topology of lattice gauge fields Dirac operator index and topology of lattice gauge fields

2000-01-13

arxiv.org/abs/hep-lat/0001014v1

Chin.J.Phys. 38 (2000) 633-646

Physics

High Energy Physics

High Energy Physics - Lattice

16 pages, based on talk at Chiral'99 (Sept. 13-18, 1999, Taipei), to be published in the Proceedings

Scientific paper

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties to L\"uscher's geometrical lattice topological charge. The main new result is that it reduces to the continuum topological charge in the classical continuum limit. (This is sketched here; the full proof will be given in a sequel to this paper.) A potential application of the ideas behind fermionic lattice topological charge to deriving a combinatorial construction of the signature invariant of a 4-manifold is also discussed.

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