Renormalizable noncommutative quantum field theory

Abstract

We discuss special Euclidean noncommutative ϕ4-quantum field theory models in two and four dimensions They are examples of renormalizable field theories. Using a Ward identity, it has been shown, that the beta function for the coupling constant vanishes to all orders in perturbation theory.We extend this work and 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. We obtain such relations for the four as well for the two dimensional situation. We expect to learn about renormalisation from this almost solvable models.