On some New Developments in Quantum Field Theory

Quantum Field Theory needs regularization and renormalization. In order to cure diseases, ideas from Noncommutative Geometry might help. Three types of deformations are used. - We mention matrix geometry and the Fuzzy Sphere; a regularization is found which respects symmetries. - Field theory on noncommutative spaces has still divergences. Recent attempts to prove renormalizability are reviewed too.