No UV/IR Mixing in Unitary Space-Time Noncommutative Field Theory

TL;DR

This paper demonstrates that unitary space-time noncommutative phi^4-theory avoids the UV/IR mixing problem, providing new Feynman rules and promising directions for systematic renormalization of such theories.

Contribution

It introduces a new approach using IPTOPT to show the absence of UV/IR mixing in noncommutative phi^4-theory and derives simplified Feynman rules.

Findings

No UV/IR mixing observed in calculated amplitudes

Derived Feynman rules facilitate diagrammatic calculations

Results suggest potential for systematic renormalization

Abstract

In this article we calculate several divergent amplitudes in phi^4-theory on non-commutative space-time in the framework of Interaction Point Time Ordered Perturbation Theory (IPTOPT), continuing work done in hep-th/0209253. On the ground of these results we find corresponding Feynman rules which allow for a much easier diagrammatic calculation of amplitudes. The most important feature of the present theory is the lack of the UV/IR mixing problem in all amplitudes calculated so far. Although we are not yet able to give a rigorous proof, we provide a strong argument for this result to hold in general. Together with the found Feynman rules this opens promising vistas towards the systematic renormalization of non-commutative field theories.