Progress in solving a noncommutative quantum field theory in four dimensions

Details Progress in solving a noncommutative quantum field theory in four dimensions Progress in solving a noncommutative quantum field theory in four dimensions

2009-09-08

arxiv.org/abs/0909.1389v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LaTeX with xy-pic

Scientific paper

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

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