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

2008/06/30 by Joseph Ben Geloun, Adrian Tanasa · 13 citations
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Commutative property #Coupling constant #Effective action #Interpretation (philosophy) #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Scalar (mathematics) #Scalar field #hep-th #math-ph #math.MP #msc:46L65 #msc:53D55 #msc:76F30 #msc:81T75

paper · pdf · doi:10.1007/s11005-008-0270-7

published in Letters in Mathematical Physics 86(1), 19-32 (Springer Science+Business Media) · 13 pages, 3 figures

arxiv created 2008/09/15 · openalex publication_date 2008/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Recently, a new type of renormalizable ϕ^{⋆ 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/(θ²p²) 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 behaviour as the one of the ϕ⁴ model on the commutative ℝ⁴. The β_a function of the new parameter a is also calculated. Some interpretation of these results are done.

Citations

• Parametric Representation of “Covariant” Noncommutative QFT Models
• Parametric Representation of Noncommutative Field Theory

Cited by

• Loop calculations for the non-commutative U ⋆(1) gauge field model with oscillator term
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory