Progress in solving a noncommutative quantum field theory in four dimensions

TL;DR

This paper advances the understanding of a four-dimensional noncommutative quantum field theory by deriving integral equations for correlation functions, enabling direct computation without traditional Feynman diagram methods.

Contribution

It introduces a novel approach to solve the noncommutative _4 quantum field theory using integral equations derived from Ward identities and Schwinger-Dyson equations, bypassing standard renormalization procedures.

Findings

Renormalisable to all orders without Landau ghost

Derived integral equations for two- and four-point functions

Facilitated direct computation of correlation functions

Abstract

We study the noncommutative \phi^4_4-quantum field theory at the self-duality point. This model is renormalisable to all orders as shown in earlier work of us and does not have a Landau ghost problem. Using the Ward identity of Disertori, Gurau, Magnen and Rivasseau, we obtain from the Schwinger-Dyson equation a non-linear integral equation for the renormalised two-point function alone. The non-trivial renormalised four-point function fulfils a linear integral equation with the inhomogeneity determined by the two-point function. These integral equations are the starting point for a perturbative solution. In this way, the renormalised correlation functions are directly obtained, without Feynman graph computation and further renormalisation steps