Noncommutative Quantum Field theory and Renormalization

The hope that ncQFT will cure the old diseases of undeformed QFT are not fulfilled, especially due to the occurence of the IR/UV mixing. We first give the definition of various deformed spaces, give the dictionany from undeformed to deformed formulations and define nc quantum field theoretic models. The IR/UV mixing property is mentioned. For the special case of a duality covariant four dimensional nc scalar QFT we proof perturbative renormalizability to all orders. This model is related to a dynamical matrix model. At the self duality point it becomes integrable and asymptotically free.