Journal of Noncommutative Geometry
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Published online: 2010-09-01
Quantum field theory on the degenerate Moyal spaceHarald Grosse and Fabien Vignes-Tourneret (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