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. By taking finite differences we reduce the infinite number of possible two point and four point functions to only two relevant/marginal operators, thus completing the proof. At a special point of the parameter space the model becomes self-dual, the beta function vanishes and the model connects to integrable systems.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Grosse, H., Wulkenhaar, R. (2006). Noncommutative QFT and Renormalization. In: Fauser, B., Tolksdorf, J., Zeidler, E. (eds) Quantum Gravity. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7978-0_16
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DOI: https://doi.org/10.1007/978-3-7643-7978-0_16
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7977-3
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