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Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere

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G. Alexanian, A. Pinzul, A. Stern

High Energy Physics - Theory · Submitted 23 Oct 2000

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

The authors' main claim We construct a star product associated with an arbitrary two dimensional Poisson structure using generalized coherent states on the complex plane.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-th/0010187 (version 2)
Pith IDITXT5A4S, Pith's permanent record of this paper and its review
CitationA. Pinzul, A. Stern, G. Alexanian. "Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere." arXiv:hep-th/0010187 (2000). https://pith.science/paper/ITXT5A4S
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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, 2,940 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.55 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We construct a star product associated with an arbitrary two dimensional Poisson structure using generalized coherent states on the complex plane. From our approach one easily recovers the star product for the fuzzy torus, and also one for the fuzzy sphere. For the latter we need to define the `fuzzy' stereographic projection to the plane and the fuzzy sphere integration measure, which in the commutative limit reduce to the usual formulae for the sphere.

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 construct a star product associated with an arbitrary two dimensional Poisson structure using generalized coherent states on the complex plane. contribution 0.96 0.95 0.52 asserted 1.00
s1 From our approach one easily recovers the star product for the fuzzy torus, and also one for the fuzzy sphere. result 0.96 0.89 0.33 asserted 0.98
s2 For the latter we need to define the `fuzzy' stereographic projection to the plane and the fuzzy sphere integration measure, which in the commutative limit reduce to the usual formulae for the sphere. method 0.80 0.84 0.12 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.75 · evidence from proof or derivation 1.00.

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not examined
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  • 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 construct a star product associated with an arbitrary two dimensional Poisson structure using generalized coherent states on the complex plane. From our approach one easily recovers the star product for the fuzzy torus, and also one for the fuzzy sphere. For the latter we need to define the `fuzzy' stereographic projection to the plane and the fuzzy sphere integration measure, which in the commutative limit reduce to the usual formulae for the sphere.

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References
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4 arXiv papers cite this in 4 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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Cites it as support 1 paper
  • The two products are equivalent in a precise technical sense: there is an invertible map [ref] T(f)=∑_n θ^n t_n(f) with the $t_n$ differential operators, such that T(fg)=T(f)T(g) where T=^θ/4∇^2 Therefore the two products define the same deformed algebra.

    Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products · Classical Free Field Theory · 0.97

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