Commutative limit of a renormalizable noncommutative model

Abstract

Renormalizable ${\varphi }_4^{\star 4}$ 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 uv/ir mixing in general Feynman graphs.

11 pages, 3 figures, minor misprints being corrected

References in corpus (12)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Noncommutative Induced Gauge Theory
• A translation-invariant renormalizable non-commutative scalar model
• Induced Gauge Theory on a Noncommutative Space
• Vacuum configurations for renormalizable non-commutative scalar models
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Translation-invariant models for non-commutative gauge fields
• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Overview of the parametric representation of renormalizable non-commutative field theory
• Parametric representation of "critical" noncommutative QFT models
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• Macroscopic Screening of Coulomb Potentials From UV/IR-Mixing

Cited by in corpus (1)

• Parametric representation of a translation-invariant renormalizable noncommutative model