Journal of Noncommutative Geometry

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Volume 4, Issue 4, 2010, pp. 555–576
DOI: 10.4171/JNCG/66

Published online: 2010-09-01

Quantum field theory on the degenerate Moyal space

Harald Grosse[1] and Fabien Vignes-Tourneret[2]

(1) University of Vienna
(2) IHES, Bures-sur-Yvette

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.

Keywords: Non-commutative geometry, quantum field theory, renormalization, Moyal space

Grosse Harald, Vignes-Tourneret Fabien: Quantum field theory on the degenerate Moyal space. J. Noncommut. Geom. 4 (2010), 555-576. doi: 10.4171/JNCG/66