  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.
