Renormalization of Non-Commutative $\Phi^4_4$ Field Theory in $x$ Space

Abstract : In this paper we provide a new proof that the Grosse-Wulkenhaar non-commutative scalar $\Phi^4_4$ theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies solely on a multiscale analysis in $x$ space. We think this proof is simpler and could be more adapted to the future study of these theories (in particular at the non-perturbative or constructive level).
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Razvan Gurau, Jacques Magnen, Vincent Rivasseau, Fabien Vignes-Tourneret. Renormalization of Non-Commutative $\Phi^4_4$ Field Theory in $x$ Space. Communications in Mathematical Physics, Springer Verlag, 2006, 267, pp.515-542. ⟨hal-00016253⟩

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