The Index of a Ginsparg-Wilson Dirac operator

Ting-Wai Chiu

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The Index of a Ginsparg-Wilson Dirac operator

Ting-Wai Chiu

High Energy Physics - Lattice · Submitted 19 Jun 2001

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configurations.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,338 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.73 · human participants 0.01 · controlled comparison 0.23 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; show every role.

A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configurations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed.	contribution 0.95	0.52	0.06	asserted 0.58
s1	Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configurations.	result 0.98	0.61	0.82	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.69.

What was examined, and what was not

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arXiv listing abstract v5

not examined

full text
figures and tables
references and citing sentences
relations to other papers

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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configurations.

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References

How the literature uses it

3 arXiv papers cite this in 19 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Unlike the Dirac operator for massless fermions in the continuum, this Ginsparg-Wilson lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configurations.

The Index and Axial Anomaly of a lattice Dirac operator · 1.00

Papers citing it · 18 sentences without a confident label

Cites it as support 1 paper

Throughout this work I will assume without proof or discussion that the index of the lattice overlap operator matches the index of the continuum operator as long as the lattice spacing is sufficiently fine[This has been demonstrated for the finite volume torus [ref] and certain infinite volume settings [ref] , although in an infinite volume the issue is non-trivial and depends to an extent on the gauge field and choice of kernel, for example, see the discussion in [ref] .].

A renormalisation group derivation of the overlap formulation · Block renormalisation group transformations · 0.96

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