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

Razvan Gurau (1) , Jacques Magnen (2) , Vincent Rivasseau (1) , Fabien Vignes-Tourneret (1)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 CPHT - Centre de Physique Théorique [Palaiseau]

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).

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

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, 2006, 267, pp.515-542. ⟨hal-00016253⟩