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On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Axel de Goursac. On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a47/

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