Abstract
We discuss a special Euclidean [Formula: see text]-quantum field theory over quantized space-time as an example of a renormalizable field theory. Using a Ward identity, it was possible to prove the vanishing of the beta function for the coupling constant to all orders in perturbation theory. We extend this work and obtain from the Schwinger-Dyson equation a non-linear integral equation for the renormalized two-point function alone. The non-trivial renormalized four-point function fulfils a linear integral equation with the inhomogeneity determined by the two-point function. These integral equations might be the starting point of a nonperturbative construction of a Euclidean quantum field theory on a noncommutative space. We expect to learn about renormalization from this almost solvable model.
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