New perturbative approximation applied to a self-interacting scalar field theory.

Abstract

A recently proposed new perturbation technique is applied to a \ensuremath{\lambda}(${\ensuremath{\varphi}}^{2}$${)}^{1+\ensuremath{\delta}}$ self-interacting scalar field theory in D-dimensional space-time. We calculate, to second order in powers of \ensuremath{\delta}, not only the two-point and the four-point Green's functions but also the (2+2\ensuremath{\delta})-point Green's function, which can be defined in this approximation. After the renormalization procedures are carried out to this order, we find that the theory is not fully nontrivial for D\ensuremath{\ge}2.