New nonperturbative calculation: Renormalization and the triviality of (λφ4)4field theory

Using a recently proposed perturbation scheme we examine a λ(${\phi }^2$ ${)}^{1+\delta }$ self-interacting scalar-field theory in d-dimensional space-time. We compute the two-point and four-point Green’s functions to second order in powers of δ. First, we carry out the renormalization program to leading order in powers of δ. We obtain a nontrivial field theory for d<4. On the other hand, our analysis suggests strongly that when d>4 the theory is free. The situation remains essentially unchanged to second order in powers of δ.