Aspects of the Renormalization of Noncommutative Yang-Mills Theories

Being an example for the intersection of noncommutative geometry with quantum field theory, Yang-Mills theory on noncommutative space-time characterized by a constant field \theta became recently very attractive. Reasons are the possibility to perform explicit calculations, their very strange results and the even more mysterious Seiberg-Witten map between noncommutative and commutative field theories. The talk will cover the infrared problems when treating \theta nonperturbatively, the ultraviolet problems when expanding the action in \theta and the noncommutative Lorentz transformations as the origin of the Seiberg-Witten map.