Noncommutative geometry as a regulator - art. no. 025004

We give a perturbative quantization of R-4 space-time in the case where the commutators C-muv = [X-mu,X-v] of the underlying algebra generators are no t central. We argue that this kind of quantum space-time can be used as a r egulator for quantum field theories. In particular we show, in the case of phi (4) theory, that by choosing appropriately the commutators C-mu ,C-v we can remove all the infinities by reproducing all the counterterms. In othe r words, the renormalized action on R-4 plus the counterterms can be rewrit ten as only a renormalized action on the quantum space-time QR(4). We conje cture therefore that the renormalization of quantum field theory is equival ent to the quantization of the underlying space-time R-4.