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Letters in Mathematical Physics

, Volume 71, Issue 1, pp 13–26 | Cite as

Renormalisation of Φ4-Theory on Non-Commutative \(\mathbb{R}^{4}\) to All Orders

  • Harald Grosse
  • Raimar Wulkenhaar
Article

Abstract

We present the main ideas and techniques of the proof that the duality-covariant four-dimensional non-commutative Φ4-model is renormalisable to all orders. This includes the reformulation as a dynamical matrix model, the solution of the free theory by orthogonal polynomials as well as the renormalisation byflow equations involving power-counting theorems for ribbon graphs drawn on Riemann surfaces

Keywords

quantum field theory renormalisation non-commutative geometry special functions 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität WienWienAustria
  2. 2.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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