JournalsjncgVol. 4 , No. 4DOI 10.4171/jncg/66

Quantum field theory on the degenerate Moyal space

  • Harald Grosse

    University of Vienna
  • Fabien Vignes-Tourneret

    IHES, Bures-sur-Yvette
Quantum field theory on the degenerate Moyal space cover

Abstract

We prove that the self-interacting scalar field on the four-dimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangian. Despite the apparent simplicity of the model, it raises several non-trivial questions. Our result is a first step towards the definition of renormalisable quantum field theories on a non-commutative Minkowski space.