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 |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| 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| _version_ | 1862701016614436864 |
|---|---|
| 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. |
| collection | DSpace DC |
| 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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| first_indexed | 2025-12-07T16:41:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146323 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:41:21Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |