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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2010 Volume 6, 048, 20 pp. (Mi sigma505)

This article is cited 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.

MSC: 81T13; 81T15; 81T75

Received: March 30, 2010; in final form June 1, 2010; Published online June 9, 2010

Language: English

DOI: 10.3842/SIGMA.2010.048



Bibliographic databases:
ArXiv: 1003.5788


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