Renormalisation of Noncommutative Quantum Field Theories

We sketch our proof that the real Euclidean ⁴-model on the four-dimensional Moyal plane is renormalisable to all orders. The bare action of relevant and marginal couplings of the model is parametrised by four (divergent) quantities which require normalisation to the experimental data. The corresponding physical parameters are the mass, the field amplitude (to be normalised to 1), the coupling constant and—in addition to the commutative version—the frequency of a harmonic oscillator potential.