Quantum Field Theory on the Noncommutative Plane with $E_q(2)$ Symmetry

A. Demichev; M. Chaichian; P. Presnajder

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Quantum Field Theory on the Noncommutative Plane with $E_q(2)$ Symmetry

M. Chaichian, A. Demichev, P. Presnajder

High Energy Physics - Theory · Submitted 20 Apr 1999

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

The authors' main claim With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane.

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arXiv IDhep-th/9904132 (version 1)

Pith IDVWDNZ7H7, Pith's permanent record of this paper and its review

CitationA. Demichev, M. Chaichian, P. Presnajder. "Quantum Field Theory on the Noncommutative Plane with $E_q(2)$ Symmetry." arXiv:hep-th/9904132 (1999). https://pith.science/paper/VWDNZ7H7

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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, 4,373 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.74 · human participants 0.01 · controlled comparison 0.27 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.88 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we define quantum fields depending on noncommutative coordinates and construct a field theoretical action using the $E_q(2)$-invariant measure on the noncommutative plane. With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane. Finally, we introduce the symmetry transformations of physical states on noncommutative spaces and discuss them in detail for the case of the $E_q(2)$ quantum group.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry.	contribution 0.98	0.90	0.05	asserted 0.80
s1	We start from the consideration of a firstly quantized quantum particle on the noncommutative plane.	method 0.95	0.70	0.02	asserted 0.84
s2	Then we define quantum fields depending on noncommutative coordinates and construct a field theoretical action using the $E_q(2)$-invariant measure on the noncommutative plane.	method 0.92	0.94	0.04	asserted 0.99
s3	With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane.	result 0.98	0.94	0.77	asserted 1.00
s4	Finally, we introduce the symmetry transformations of physical states on noncommutative spaces and discuss them in detail for the case of the $E_q(2)$ quantum group.	contribution 0.99	0.92	0.05	asserted 0.86

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

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arXiv listing abstract v1

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full text
figures and tables
references and citing sentences
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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 study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we define quantum fields depending on noncommutative coordinates and construct a field theoretical action using the $E_q(2)$-invariant measure on the noncommutative plane. With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane. Finally, we introduce the symmetry transformations of physical states on noncommutative spaces and discuss them in detail for the case of the $E_q(2)$ quantum group.

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References

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

String Theory and Noncommutative Geometry
hep-th 1999-08 accept novelty 9.0 of 10

Open strings in a constant B-field are described by noncommutative Yang-Mills theory in a zero-slope limit, and that theory is equivalent to ordinary Yang-Mills theory through an explicit change of variables.
Noncommutative Perturbative Dynamics
hep-th 1999-12 accept novelty 8.0 of 10

In noncommutative field theories, high-energy virtual particles in loops generate singularities at zero momentum, so the low-energy effective action is singular even when the theory is massive.

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Papers whose main result relates to this one's

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Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

As a result the theory is UV finite and the cutoff is provided by the noncommutative parameter theta.

UV divergence-free QFT on noncommutative plane · 0.96

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