Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 048, 20 pages      arXiv:1003.5788      https://doi.org/10.3842/SIGMA.2010.048
Contribution to the Special Issue “Noncommutative Spaces and Fields”

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

Received March 30, 2010, in final form June 01, 2010; Published online June 09, 2010

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.

Key words: noncommutative QFT; gauge theory; renormalization; Heisenberg algebra.

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