New nonperturbative calculation: Renormalization and the triviality of ( lambda phi4)4 field theory.

Abstract

Using a recently proposed perturbation scheme we examine a \ensuremath{\lambda}(${\ensuremath{\varphi}}^{2}$${)}^{1+\ensuremath{\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 \ensuremath{\delta}. First, we carry out the renormalization program to leading order in powers of \ensuremath{\delta}. 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 \ensuremath{\delta}.