Bulg. J. Phys. vol.33 no.s1 (2006), pp. 215-225

Noncommutative QFT and Renormalization

H. Grosse1, R. Wulkenhaar2
1Universität Wien, Institut für Theoretische Physik Boltzmanngasse 5, A-1090 Wien, Austria
2Universität Münster, Mathematisches Institut Einsteinstrasse 62, D-48149 Münster, Germany
Abstract. Since the two pillars of modern physics: Quantum Field Theory and general relativity are incompatible, one tries to take fluctuating geometries into account through deforming space-time. The resulting noncommutative Quantum Field Theory shows the IR/UV mixing. We modify the action for a scalar model in 4 dimensions and show, that a renormalizable field theory results. For the proof we fist transform to a matrix model and use the Wilson- Polchinski approach to renormalization. An efficient power-counting theorem allows to eliminate all higher genus contributions. At a special point of the parameter space the model becomes self-dual, the beta function vanishes and the model connects to integrable systems.

Full-text: PDF

go back