Why Renormalizable NonCommutative Quantum Field Theories?

TL;DR

This paper reviews noncommutative quantum field theories, focusing on the Grosse-Wulkenhaar model, and proposes that combining multiple high-energy theories could lead to an effective low-energy commutative field theory.

Contribution

It provides a comprehensive review of noncommutative field theories and introduces a novel idea of constructing effective commutative theories from high-energy noncommutative models.

Findings

Complete review of noncommutative field theories

Discussion of the constructive approach to Grosse-Wulkenhaar theory

Proposal for deriving effective commutative theories from high-energy noncommutative models

Abstract

We complete our previous recent review on noncommutative field theory, discussing in particular the constructive aproach to the Grosse-Wulkenhaar theory. We also suggest that by gluing together many Grosse-Wulkenhaar theories at high energy one can obtain an effective commutative field theory at lower energy.