Volume 86, Number 1, April 2009
Article Number 11001
Number of page(s) 6
Section The Physics of Elementary Particles and Fields
Published online 22 April 2009
EPL, 86 (2009) 11001
DOI: 10.1209/0295-5075/86/11001

Commutative limit of a renormalizable noncommutative model

J. Magnen1, V. Rivasseau2 and A. Tanasa1, 3

1   Centre de Physique Théorique, CNRS UMR 7644, Ecole Polytechnique - 91128 Palaiseau, France, EU
2   Laboratoire de Physique Théorique, CNRS UMR 8627, bât. 210, Université Paris XI - 91405 Orsay Cedex, France, EU
3   Institutul de Fizica si Inginerie Nucleara Horia Hulubei - P. O. Box MG-6, 077125 Bucuresti-Magurele, Romania, EU

received 20 February 2009; accepted in final form 16 March 2009; published April 2009
published online 22 April 2009

Renormalizable $\phi ^{\star 4}_{4}$ models on Moyal space have been obtained by modifying the commutative propagator. But these models have a divergent “naive” commutative limit. We explain here how to obtain a coherent such commutative limit for a recently proposed translation-invariant model. The mechanism relies on the analysis of the ultraviolet/infrared mixing in Feynman graphs at any order in perturbation theory.

11.10.Nx - Noncommutative field theory.

© EPLA 2009