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The Absence of Ultralocal Ginsparg-Wilson Fermions
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It was shown recently by I. Horvath that lattice fermions obeying the standard form of the Ginsparg-Wilson relation cannot be ultralocal. However, there are more general forms of the Ginsparg-Wilson relation, which also guarantee the physical properties related to chirality, but which are not covered by Horvath's consideration. Here we present a proof which applies to all Ginsparg-Wilson fermions, demonstrating that they can only be local in the sense of an exponential decay of their couplings, but not ultralocal.
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Cited by 2 Pith papers
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Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions
Physics-informed neural networks construct overlap fermions by optimizing to the Ginsparg-Wilson relation and autonomously discover both the standard and generalized Fujikawa-type versions of the relation.
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Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions
Physics-Informed Neural Networks construct lattice Dirac operators satisfying the Ginsparg-Wilson relation, reproducing overlap fermions to high accuracy and discovering a Fujikawa-type generalized relation via algebr...
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