Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space

TL;DR

This paper presents a simplified multiscale analysis proof demonstrating the all-order renormalizability of the Grosse-Wulkenhaar non-commutative Phi^4_4 theory in x space, extending to models with covariant derivatives.

Contribution

It provides a new, simpler proof of renormalizability for non-commutative scalar field theory using x space analysis, applicable to more general models.

Findings

Proof of all-order renormalizability in x space

Extension to models with covariant derivatives

Potential for non-perturbative analysis

Abstract

In this paper we provide a new proof that the Grosse-Wulkenhaar non-commutative scalar Phi^4_4 theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies solely on a multiscale analysis in x space. We think this proof is simpler and could be more adapted to the future study of these theories (in particular at the non-perturbative or constructive level).