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

A recently proposed new perturbation technique is applied to a λ(${\phi }^2$ ${)}^{1+\delta }$ self-interacting scalar field theory in D-dimensional space-time. We calculate, to second order in powers of δ, not only the two-point and the four-point Green’s functions but also the (2+2δ)-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≥2.