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SIGMA, 2010, Volume 6, 048, 20 pages (Mi sigma505)  

This article is cited in 10 scientific papers (total in 10 papers)

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

Axel de Goursac

Département de Mathématiques, Université Catholique de Louvain, Chemin du Cyclotron, 2, 1348 Louvain-la-Neuve, Belgium

Abstract: 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.

Keywords: noncommutative QFT; gauge theory; renormalization; Heisenberg algebra

DOI: https://doi.org/10.3842/SIGMA.2010.048

Full text: PDF file (385 kB)
Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/048/
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Bibliographic databases:

ArXiv: 1003.5788
MSC: 81T13; 81T15; 81T75
Received: March 30, 2010; in final form June 1, 2010; Published online June 9, 2010
Language:

Citation: Axel de Goursac, “On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory”, SIGMA, 6 (2010), 048, 20 pp.

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. de Goursac A., Wallet J.-Ch., “Symmetries of noncommutative scalar field theory”, Journal of Physics a-Mathematical and Theoretical, 44:5 (2011), 055401  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Buric M. Dimitrijevic M. Radovanovic V. Wohlgenannt M., “Quantization of Gauge Theory on a Curved Noncommutative Space”, Phys. Rev. D, 86:10 (2012), 105024  crossref  mathscinet  adsnasa  isi  scopus
    3. Bieliavsky P., de Goursac A., Tuynman G., “Deformation Quantization for Heisenberg Supergroup”, J. Funct. Anal., 263:3 (2012), 549–603  crossref  mathscinet  zmath  isi  scopus
    4. de Goursac A., Masson T., Wallet J.-Ch., “Noncommutative Epsilon-Graded Connections”, J. Noncommutative Geom., 6:2 (2012), 343–387  crossref  mathscinet  zmath  isi  scopus
    5. de Goursac A., “Renormalization of the Commutative Scalar Theory with Harmonic Term to All Orders”, Ann. Henri Poincare, 14:8 (2013), 2025–2043  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Blaschke D.N. Grosse H. Wallet J.-Ch., “Slavnov-Taylor Identities, Non-Commutative Gauge Theories and Infrared Divergences”, J. High Energy Phys., 2013, no. 6, 038  crossref  mathscinet  zmath  isi  elib  scopus
    7. Blaschke D.N. Garschall T. Gieres F. Heindl F. Schweda M. Wohlgenannt M., “On the Renormalization of Non-Commutative Field Theories”, Eur. Phys. J. C, 73:1 (2013), 2262  crossref  adsnasa  isi  scopus
    8. de Goursac A., “Frechet Quantum Supergroups”, Pac. J. Math., 273:1 (2015), 169–195  crossref  mathscinet  zmath  isi  scopus
    9. Buric M. Madore J. Nenadovic L., “Spinors on a Curved Noncommutative Space: Coupling To Torsion and the Gross-Neveu Model”, Class. Quantum Gravity, 32:18 (2015), 185018  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. de Goursac A., “Noncommutative Supergeometry and Quantum Supergroups”, Xxxth International Colloquium on Group Theoretical Methods in Physics (Icgtmp) (Group30), Journal of Physics Conference Series, 597, IOP Publishing Ltd, 2015, 012028  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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