On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory

The harmonic term in the scalar field theory on the Moyal space removes the UV-IR mixing, so that the theory is renormalizable to all orders. In this paper, we review the three principal interpretations of this harmonic term: the Langmann-Szabo duality, the superalgebraic approach and the noncommuta...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2010
Main Author: Goursac, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2010
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/146323
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory / A. Goursac // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 62 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Goursac, A.
author_facet Goursac, A.
citation_txt On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory / A. Goursac // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 62 назв. — англ.
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container_title Symmetry, Integrability and Geometry: Methods and Applications
description The harmonic term in the scalar field theory on the Moyal space removes the UV-IR mixing, so that the theory is renormalizable to all orders. In this paper, we review the three principal interpretations of this harmonic term: the Langmann-Szabo duality, the superalgebraic approach and the noncommutative scalar curvature interpretation. Then, we show some deep relationship between these interpretations.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2025-12-07T16:41:21Z
publishDate 2010
publisher Інститут математики НАН України
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spelling Goursac, A.
2019-02-08T20:55:14Z
2019-02-08T20:55:14Z
2010
On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory / A. Goursac // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 62 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 81T13; 81T15; 81T75
DOI:10.3842/SIGMA.2010.048
https://nasplib.isofts.kiev.ua/handle/123456789/146323
The harmonic term in the scalar field theory on the Moyal space removes the UV-IR mixing, so that the theory is renormalizable to all orders. In this paper, we review the three principal interpretations of this harmonic term: the Langmann-Szabo duality, the superalgebraic approach and the noncommutative scalar curvature interpretation. Then, we show some deep relationship between these interpretations.
This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html.
 The author thanks Pierre Bieliavsky and Jean-Christophe Wallet for interesting discussions at various stages of this work. This work was supported by the Belgian Interuniversity Attraction Pole (IAP) within the framework “Nonlinear systems, stochastic processes, and statistical mechanics” (NOSY).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
Article
published earlier
spellingShingle On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
Goursac, A.
title On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
title_full On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
title_fullStr On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
title_full_unstemmed On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
title_short On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
title_sort on the origin of the harmonic term in noncommutative quantum field theory
url https://nasplib.isofts.kiev.ua/handle/123456789/146323
work_keys_str_mv AT goursaca ontheoriginoftheharmonicterminnoncommutativequantumfieldtheory