Commutative limit of a renormalizable noncommutative model

TL;DR

This paper presents a method to achieve a consistent commutative limit in a renormalizable noncommutative quantum field theory by analyzing UV/IR mixing effects, addressing divergence issues in previous models.

Contribution

It introduces a new approach to obtain a coherent commutative limit for a translation-invariant noncommutative model, improving upon previous models with divergent limits.

Findings

Successfully derived a coherent commutative limit

Analyzed UV/IR mixing in Feynman graphs

Resolved divergence issues in noncommutative models

Abstract

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