Scalar and gauge translation-invariant noncommutative models

TL;DR

This paper reviews recent progress on translation-invariant noncommutative models, highlighting a renormalizable scalar model, its properties, and a proposed gauge model, advancing the understanding of noncommutative quantum field theories.

Contribution

It provides an overview of the development of translation-invariant noncommutative models, including a renormalizable scalar model and a proposed gauge model.

Findings

Scalar model proven renormalizable

One-loop renormalization group flow calculated

A mechanism for the commutative limit proposed

Abstract

We make here a short overview of the recent developments regarding translation-invariant models on the noncommutative Moyal space. A scalar model was first proposed and proved renormalizable. Its one-loop renormalization group flow and parametric representation were calculated. Furthermore, a mechanism to take its commutative limit was recently given. Finally, a proposition for a renormalizable, translation-invariant gauge model was made.