Preserving unitarity in a novel perturbative technique for solving quantum field theory

A new perturbative technique for solving a scalar φ2 P theory consists of expanding a φ2(1+δ) interaction in powers of δ. The Green functions are computed as a power series in δ by applying a linear differential operator to the Green functions of a specially constructed intermediate Lagrangian. We confront this linear procedure with the quadratic requirement of perturbative unitarity. We verify up to order δ3 that unitarity is indeed satisfied, by virtue of the precise structure of the intermediate Lagrangian. Unitarity gives constraints on that structure, but does not fix it uniquely. © 1989 Springer-Verlag.