Letters in Mathematical Physics

, Volume 86, Issue 1, pp 19–32 | Cite as

One-Loop β Functions of a Translation-Invariant Renormalizable Noncommutative Scalar Model

  • Joseph Ben Geloun
  • Adrian Tanasa


Recently, a new type of renormalizable \({\phi^{\star 4}_{4}}\) scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a a/(θ 2 p 2) term. We calculate here the β and γ functions at one-loop level for this model. The coupling constant β λ function is proved to have the same behavior as the one of the \({\phi^4}\) model on the commutative \({\mathbb{R}^4}\) . The β a function of the new parameter a is also calculated. Some interpretation of these results are done.

Mathematics Subject Classification (2000)

76F30 81T75 46L65 53D55 


noncommutative quantum field theory renormalization β function 


02.40.Gh 11.10.Nx 


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Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.International Chair of Mathematical Physics and ApplicationsUniversité d’Abomey-Calavi, ICMPA-UNESCO ChairCotonouRepublic of Benin
  2. 2.Faculté des Sciences et Techniques, Dpt. Mathématiques-InformatiqueUniversité Cheikh Anta DiopDakarSenegal
  3. 3.Laboratoire de Physique ThéoriqueUMR CNRS 8627 bât. 210, Université Paris-Sud X1OrsayFrance
  4. 4.Departamentul de Fizica TeoreticăInstitutul de Fizica si Inginerie Nucleară Horia HulubeiBucureşti-MăgureleRomania
  5. 5.Institut des Hautes Études Scientifiques (IHÉS), Le Bois-MarieBures-sur-YvetteFrance

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