# 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).
Document type :
Journal articles
Domain :

Cited literature [18 references]

https://hal.archives-ouvertes.fr/hal-00016253
Contributor : Responsable Bibliotheque <>
Submitted on : Friday, February 15, 2019 - 12:08:31 PM
Last modification on : Friday, May 10, 2019 - 3:02:05 PM
Long-term archiving on : Friday, May 17, 2019 - 12:14:18 PM

### File

newxspace.pdf
Files produced by the author(s)

### Citation

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⟩

Record views