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An Isaac Newton Institute Workshop

Noncommutative Geometry and Physics: Fundamental Structure of Space and Time

Renormalisation of quantum field theories on noncommutative geometries

Author: Raimar Wulkenhaar (Math.Inst, Univ. Münster)

Abstract

I am going to review the recent progress on the renormalisation programme for quantum field theories on the Moyal plane. There are now three different proofs that the noncommutative \phi^4_4-model, extended by a harmonic oscillator potential to reflect the UV/IR-entanglement, is renormalisable to all orders in perturbation theory. The behaviour of the \beta-function indicates that a rigorous construction of this model might be possible.

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