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Locality properties of Neuberger’s lattice Dirac operator. (English) Zbl 0958.81054

Summary: The gauge covariant lattice Dirac operator \(D\) which has recently been proposed by Neuberger satisfies the Ginsparg-Wilson relation and thus preserves chiral symmetry. The operator also avoids a doubling of fermion species, but its locality properties are not obvious. We now prove that \(D\) is local (with exponentially decaying tails) if the gauge field is sufficiently smooth at the scale of the cutoff. Further analytic and numerical studies moreover suggest that the locality of the operator is in fact guaranteed under far more general conditions.

MSC:

81T25 Quantum field theory on lattices
81T13 Yang-Mills and other gauge theories in quantum field theory
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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