Ultraviolet-infrared mixing on the noncommutative Minkowski space in the Yang-Feldman formalism

TL;DR

This paper investigates the severe infrared divergences caused by ultraviolet-infrared mixing in quantum field theories on noncommutative Minkowski space, revealing worse issues than in Euclidean cases and discussing renormalization challenges.

Contribution

It provides the first analysis of ultraviolet-infrared mixing in Lorentzian noncommutative quantum field theories within the Yang-Feldman formalism, highlighting new divergences.

Findings

Infrared divergences are more severe in Lorentzian signature than Euclidean.

Graphs finite in Euclidean models exhibit divergences in Minkowski space.

Adapting nonlocal counterterms for renormalization faces significant obstacles.

Abstract

We study infrared divergences due to ultraviolet-infrared mixing in quantum field theory on Moyal space with Lorentzian signature in the Yang-Feldman formalism. Concretely, we are considering the phi^4 and the phi^3 model in arbitrary even dimension. It turns out that the situation is worse than in the Euclidean setting, in the sense that we find infrared divergences in graphs that are finite there. We briefly discuss the problems one faces when trying to adapt the nonlocal counterterms that render the Euclidean model renormalizable.