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Renormalizable ϕ ⋆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.
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A 2009 study studied this question.
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