Non-Commutative Renormalization

Vincent Rivasseau (1) , F. Vignes-Tourneret (1)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

We review the recent approach of Grosse and Wulkenhaar to the perturbative renormalization of non commutative field theory and suggest a related constructive program. This paper is dedicated to J. Bros on his 65th birthday.

Mots clés: Quantum field theory; Renormalisation; Noncommutative geometry

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

Vincent Rivasseau, F. Vignes-Tourneret. Non-Commutative Renormalization. de Monvel A.B., Buchholz D., Iagolnitzer D., Moschella U. (eds). Rigorous Quantum Field Theory, Jul 2004, Paris, France. Progress in Mathematics, 251, pp.271-281, 2004, Rigorous Quantum Field Theory, ⟨10.1007/978-3-7643-7434-1_19⟩. ⟨hal-00124380⟩