15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion ESI - Erwin Schrödinger Institut
Dienstag, 18. September 2001, 16.00-16.50, ESI-Hörsaal


Regularization and Renormalization of Quantum Field Theory from Noncommutative Geometry

Harald Grosse, Universität Wien


Despite many attempts, quantum field theory on commutative space-time has severe shortcomings. Recently various deformations of the algebra of functions over a manifold have been considered. We review such regularization methods based on matrix geometry and show, how an ultraviolet cut-off respecting symmetries results. Nontrivial topological configurations as well as supersymmetric models can be treated as well. Next we review recent attempts to renormalize deformed quantum field theory models. We mention the IR-UV mixing which is avoided if a higher symmetry is involved. Whether the Yang-Mills model is renormalizable is still open.

E-Mail: harald.grosse@univie.ac.at

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