Quantum Corrections for Translation-Invariant Renormalizable Non-Commutative Phi^4 Theory

TL;DR

This paper demonstrates how to achieve renormalizability in a 4D non-commutative Phi^4 theory by explicitly calculating Feynman graphs, showing suppression of IR divergences and overcoming UV/IR mixing.

Contribution

It provides explicit one-loop and higher-order calculations that establish the renormalizability of translation-invariant non-commutative Phi^4 theory, addressing UV/IR mixing issues.

Findings

UV/IR mixing is overcome in the model

IR divergences are suppressed in the massless case

The results support potential gauge field generalizations

Abstract

In this paper we elaborate on the translation-invariant renormalizable Phi^4 theory in 4-dimensional non-commutative space which was recently introduced by the Orsay group. By explicitly performing Feynman graph calculations at one loop and higher orders we illustrate the mechanism which overcomes the UV/IR mixing problem and ultimately leads to a renormalizable model. The obtained results show that the IR divergences are also suppressed in the massless case, which is of importance for the gauge field theoretic generalization of the scalar field model.