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Chiral symmetry and spectrum of Euclidean Dirac operator in QCD

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A. Smilga

High Energy Physics - Theory · Submitted 8 Mar 1995

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

The authors' main claim Some exact relations for the spectral density $\rho(\lambda)$ of the Euclidean Dirac operator in $QCD$ are derived.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-th/9503049 (version 3)
Pith IDUDQ4A57K, Pith's permanent record of this paper and its review
CitationA. Smilga. "Chiral symmetry and spectrum of Euclidean Dirac operator in QCD." arXiv:hep-th/9503049 (1995). https://pith.science/paper/UDQ4A57K
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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, 3,756 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Some exact relations for the spectral density $\rho(\lambda)$ of the Euclidean Dirac operator in $QCD$ are derived. They follow directly from the chiral symmetry of the $QCD$ lagrangian with massless quarks. New results are obtained both in thermodynamic limit when the Euclidean volume $V$ is sent to infinity and also in the theory defined in finite volume where the spectrum is discrete and a nontrivial information on $\rho(\lambda)$ in the region $\lambda \sim 1/(|<\bar{q}q>_0|V)$ (the characteristic level spacing) can be obtained. These exact results should be confronted with "experimental" numerical simulations on the lattices and in some particular models for $QCD$ vacuum structure and may serve as a nontrivial test of the validity of these simulations.

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 Some exact relations for the spectral density $\rho(\lambda)$ of the Euclidean Dirac operator in $QCD$ are derived. result 0.68 0.94 0.57 asserted 1.00
s1 They follow directly from the chiral symmetry of the $QCD$ lagrangian with massless quarks. method 0.54 0.53 0.09 asserted 1.00
s2 New results are obtained both in thermodynamic limit when the Euclidean volume $V$ is sent to infinity and also in the theory defined in finite volume where the spectrum is discrete and a nontrivial information on $\rho(\lambda)$ in the region $\lambda \sim 1/(|<\bar{q}q>_0|V)$ (the characteristic level spacing) can be obtained. result 0.77 0.90 0.42 asserted 0.91
s3 These exact results should be confronted with "experimental" numerical simulations on the lattices and in some particular models for $QCD$ vacuum structure and may serve as a nontrivial test of the validity of these simulations. future work 0.93 0.15 0.16 hedged possibility 0.93

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • figures and tables
  • references and citing sentences
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  • P abstract
not run
  • 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

Some exact relations for the spectral density $\rho(\lambda)$ of the Euclidean Dirac operator in $QCD$ are derived. They follow directly from the chiral symmetry of the $QCD$ lagrangian with massless quarks. New results are obtained both in thermodynamic limit when the Euclidean volume $V$ is sent to infinity and also in the theory defined in finite volume where the spectrum is discrete and a nontrivial information on $\rho(\lambda)$ in the region $\lambda \sim 1/(|<\bar{q}q>_0|V)$ (the characteristic level spacing) can be obtained. These exact results should be confronted with "experimental" numerical simulations on the lattices and in some particular models for $QCD$ vacuum structure and may serve as a nontrivial test of the validity of these simulations.

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References
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1 arXiv paper 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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