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On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations

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Christof Gattringer, Ivan Hip

High Energy Physics - Lattice · Submitted 12 Dec 1997

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

The authors' main claim We demonstrate, that those properties of the spectrum which correspond to non-trivial topology are stable under adding fluctuations to the gauge fields.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-lat/9712015 (version 3)
Pith ID4YXQ2C2A, Pith's permanent record of this paper and its review
CitationChristof Gattringer, Ivan Hip. "On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations." arXiv:hep-lat/9712015 (1997). https://pith.science/paper/4YXQ2C2A
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The compiled record

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, 3,579 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.09 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We study characteristic features of the eigenvalues of the Wilson-Dirac operator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. In particular we discuss the role of eigenvectors with real eigenvalues as the lattice equivalents of the continuum zero-modes. We demonstrate, that those properties of the spectrum which correspond to non-trivial topology are stable under adding fluctuations to the gauge fields. The behavior of the spectrum in a fully quantized theory is discussed using QED_2 as an example.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study characteristic features of the eigenvalues of the Wilson-Dirac operator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. contribution 0.99 0.94 0.09 asserted 0.89
s1 In particular we discuss the role of eigenvectors with real eigenvalues as the lattice equivalents of the continuum zero-modes. contribution 0.74 0.49 0.11 asserted 0.79
s2 We demonstrate, that those properties of the spectrum which correspond to non-trivial topology are stable under adding fluctuations to the gauge fields. result 1.00 0.90 0.53 asserted 1.00
s3 The behavior of the spectrum in a fully quantized theory is discussed using QED_2 as an example. method 0.58 0.71 0.07 asserted 0.79

What kind of paper the classifier reports this is: simulation study 0.80 · evidence from simulation or computation 0.98.

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  • arXiv listing abstract v3
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

We study characteristic features of the eigenvalues of the Wilson-Dirac operator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. In particular we discuss the role of eigenvectors with real eigenvalues as the lattice equivalents of the continuum zero-modes. We demonstrate, that those properties of the spectrum which correspond to non-trivial topology are stable under adding fluctuations to the gauge fields. The behavior of the spectrum in a fully quantized theory is discussed using QED_2 as an example.

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References
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2 arXiv papers cite this in 2 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

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