Pith. Sign in

RECORD

Noncommutative spacetime symmetries: Twist versus covariance

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
J.M. Gracia-Bondia, Fedele Lizzi, F. Ruiz Ruiz, Patrizia Vitale

High Energy Physics - Theory · Submitted 27 Apr 2006

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

The authors' main claim We prove that the Moyal product is covariant under linear affine spacetime transformations.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDhep-th/0604206 (version 2)
Pith ID6J3K4GWG, Pith's permanent record of this paper and its review
CitationFedele Lizzi, F. Ruiz Ruiz, J.M. Gracia-Bondia, Patrizia Vitale. "Noncommutative spacetime symmetries: Twist versus covariance." arXiv:hep-th/0604206 (2006). https://pith.science/paper/6J3K4GWG
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,282 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.95 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,\Theta)$-space where the spacetime coordinates and the noncommutativity matrix components are on the same footing, we obtain a noncommutative representation of the affine algebra, its generators being differential operators in $(x,\Theta)$-space. As a particular case, the Weyl Lie algebra is studied and known results for Weyl invariant noncommutative field theories are rederived in a nutshell. We also show that this covariance cannot be extended to spacetime transformations generated by differential operators whose coefficients are polynomials of order larger than one. We compare our approach with the twist-deformed enveloping algebra description of spacetime transformations.

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 prove that the Moyal product is covariant under linear affine spacetime transformations. result 0.95 0.94 0.71 asserted 1.00
s1 From the covariance law, by introducing an $(x,\Theta)$-space where the spacetime coordinates and the noncommutativity matrix components are on the same footing, we obtain a noncommutative representation of the affine algebra, its generators being differential operators in $(x,\Theta)$-space. contribution 0.46 0.95 0.19 asserted 1.00
s2 As a particular case, the Weyl Lie algebra is studied and known results for Weyl invariant noncommutative field theories are rederived in a nutshell. contribution 0.55 0.83 0.07 asserted 0.98
s3 We also show that this covariance cannot be extended to spacetime transformations generated by differential operators whose coefficients are polynomials of order larger than one. limitation 0.56 0.95 0.26 asserted 1.00
s4 We compare our approach with the twist-deformed enveloping algebra description of spacetime transformations. contribution 0.85 0.82 0.06 asserted 0.64

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

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • 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

We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,\Theta)$-space where the spacetime coordinates and the noncommutativity matrix components are on the same footing, we obtain a noncommutative representation of the affine algebra, its generators being differential operators in $(x,\Theta)$-space. As a particular case, the Weyl Lie algebra is studied and known results for Weyl invariant noncommutative field theories are rederived in a nutshell. We also show that this covariance cannot be extended to spacetime transformations generated by differential operators whose coefficients are polynomials of order larger than one. We compare our approach with the twist-deformed enveloping algebra description of spacetime transformations.

Human review

How Pith checks papers → · Full audit of this paper →

References
How the literature uses it

7 arXiv papers cite this in 9 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 citing it · 7 sentences without a confident label

Builds on it 1 paper
  • Although here the explicit functional form of the integral kernels is given for an invertible \(θ\) (as DFR matrices are), the formalism can easily be generalised (see e.g. [ref] ) to the case of a non invertible matrix, including the case of time-space commutativity[Note however that time-space commutativity is not preserved by Lorentz transformations.].

    Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model · Introduction · 0.83

Cites it as background 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.