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

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Cited by in corpus (11)

• Multi-orientable Group Field Theory
• Multifractional theories: an unconventional review
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
• Neutrino propagation in noncommutative spacetimes
• Self-energies on deformed spacetimes
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Realization of the Noncommutative Seiberg-Witten Gauge Theory by Fields in Phase Space
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Non-abelian gauge symmetry for fields in phase space: a realization of the Seiberg-Witten non-abelian gauge theory