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On the ultraviolet behaviour of quantum fields over noncommutative manifolds

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Joseph C. Varilly, Jose M. Gracia-Bondia

High Energy Physics - Theory · Submitted 1 Apr 1998

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

The authors' main claim We analyze the ultraviolet behaviour of second-quantized fields over noncommutative 3-tori, and discuss what behaviour should be expected on other noncommutative spin manifolds.

how it is stated · asserted 0.66 read the record →

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arXiv IDhep-th/9804001 (version 2)
Pith IDHZKBHM5R, Pith's permanent record of this paper and its review
CitationJose M. Gracia-Bondia, Joseph C. Varilly. "On the ultraviolet behaviour of quantum fields over noncommutative manifolds." arXiv:hep-th/9804001 (1998). https://pith.science/paper/HZKBHM5R
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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, 2,411 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

By exploiting the relation between Fredholm modules and the Segal-Shale-Stinespring version of canonical quantization, and taking as starting point the first-quantized fields described by Connes' axioms for noncommutative spin geometries, a Hamiltonian framework for fermion quantum fields over noncommutative manifolds is introduced. We analyze the ultraviolet behaviour of second-quantized fields over noncommutative 3-tori, and discuss what behaviour should be expected on other noncommutative spin manifolds.

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 By exploiting the relation between Fredholm modules and the Segal-Shale-Stinespring version of canonical quantization, and taking as starting point the first-quantized fields described by Connes' axioms for noncommutative spin geometries, a Hamiltonian framework for fermion quantum fields over noncommutative manifolds is introduced. contribution 0.79 0.90 0.09 asserted 1.00
s1 We analyze the ultraviolet behaviour of second-quantized fields over noncommutative 3-tori, and discuss what behaviour should be expected on other noncommutative spin manifolds. contribution 0.97 0.87 0.21 asserted 0.66

What kind of paper the classifier reports this is: theoretical result 0.55 · evidence from proof or derivation 0.96.

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  • references and citing sentences
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  • T body sentences
  • C citations
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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

By exploiting the relation between Fredholm modules and the Segal-Shale-Stinespring version of canonical quantization, and taking as starting point the first-quantized fields described by Connes' axioms for noncommutative spin geometries, a Hamiltonian framework for fermion quantum fields over noncommutative manifolds is introduced. We analyze the ultraviolet behaviour of second-quantized fields over noncommutative 3-tori, and discuss what behaviour should be expected on other noncommutative spin manifolds.

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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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