Symmetries of noncommutative scalar field theory∗ Axel de Goursaca, Jean-Christophe Walletb aDépartement de Mathématiques et Physique,

We investigate symmetries of the scalar field theory with harmonic term on the Moyal space with euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can be restored also at the quantum level by restricting the symplectic structures to a particular orbit. ∗Work supported by the Belgian Interuniversity Attraction Pole (IAP) within the framework “Nonlinear sys-tems, stochastic processes, and statistical mechanics ” (NOSY). 1 a