DIMENSIONAL CROSS-OVER FROM NON-RENORMALIZABILITY TO RENORMALIZABILITY

In the context of a 'toy' Kaluza Klein model it is shown, to one loop, that lambdaphi4 theory contracts from being a non-renormalizable theo ry above four dimensions to a renormalizable theory in the limit of ze ro size of the additional dimensions above four; in particular the non renormalizable couplings scale to zero in this limit. This provides an example of the decoupling of an infinite number of modes in the infra red domain of the theory. The results also have applications to statis tical mechanical systems above the critical point in the context of fi nite size effects.