%0 Journal Article %T On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory %A Axel de Goursac %J Symmetry, Integrability and Geometry : Methods and Applications %D 2010 %I National Academy of Science of Ukraine %X 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. %K noncommutative QFT %K gauge theory %K renormalization %K Heisenberg algebra %U http://dx.doi.org/10.3842/SIGMA.2010.048