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.