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Concerning a natural compatibility condition between the action and the renormalized operator product

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Olivier de Mirleau (University of Amsterdam)

High Energy Physics - Theory · Submitted 19 Aug 1996

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

The authors' main claim Second, the compatibility can be used as the definition of a category; consideration of this category as the central object of study in quantum field theory seems to have quite some advantages over previously introduced theories of the type ``S-matrix theory'', ``Vertex operator algebras'', since this seems to be the only category in which both the action and the expectation values enter, the two being linked roughly speaking by a combination of the Frobenius property and the renormalized Schwinger-Dyson equation.

how it is stated · hedged possibility 0.71 read the record →

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arXiv IDhep-th/9608120 (version 1)
Pith IDD5AJN3SJ, Pith's permanent record of this paper and its review
CitationOlivier de Mirleau (University of Amsterdam). "Concerning a natural compatibility condition between the action and the renormalized operator product." arXiv:hep-th/9608120 (1996). https://pith.science/paper/D5AJN3SJ
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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, 3,085 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.81 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this article we note that in a number of situations the operator product and the classical action satisfy a natural compatibility condition. We consider the interest of this condition to be twofold: First, the naturality (functoriality) of the compatibility condition suggests that it be used for geometrical applications of renormalized functional integration. Second, the compatibility can be used as the definition of a category; consideration of this category as the central object of study in quantum field theory seems to have quite some advantages over previously introduced theories of the type ``S-matrix theory'', ``Vertex operator algebras'', since this seems to be the only category in which both the action and the expectation values enter, the two being linked roughly speaking by a combination of the Frobenius property and the renormalized Schwinger-Dyson equation.

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 In this article we note that in a number of situations the operator product and the classical action satisfy a natural compatibility condition. result 0.64 0.80 0.42 asserted 0.92
s1 We consider the interest of this condition to be twofold: First, the naturality (functoriality) of the compatibility condition suggests that it be used for geometrical applications of renormalized functional integration. interpretation 0.86 0.46 0.16 hedged possibility 0.85
s2 Second, the compatibility can be used as the definition of a category; consideration of this category as the central object of study in quantum field theory seems to have quite some advantages over previously introduced theories of the type ``S-matrix theory'', ``Vertex operator algebras'', since this seems to be the only category in which both the action and the expectation values enter, the two being linked roughly speaking by a combination of the Frobenius property and the renormalized Schwinger-Dyson equation. interpretation 0.55 0.37 0.50 hedged possibility 0.71

What kind of paper the classifier reports this is: position or commentary 0.95 · evidence from argument 0.97.

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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

In this article we note that in a number of situations the operator product and the classical action satisfy a natural compatibility condition. We consider the interest of this condition to be twofold: First, the naturality (functoriality) of the compatibility condition suggests that it be used for geometrical applications of renormalized functional integration. Second, the compatibility can be used as the definition of a category; consideration of this category as the central object of study in quantum field theory seems to have quite some advantages over previously introduced theories of the type ``S-matrix theory'', ``Vertex operator algebras'', since this seems to be the only category in which both the action and the expectation values enter, the two being linked roughly speaking by a combination of the Frobenius property and the renormalized Schwinger-Dyson equation.

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