The scattering matrix is non-trivial for weakly coupled P(phi)2 models

It is shown that for sufficiently small coupling constant lambda the lambdaP(phi)2 quantum field theory models have a scattering matrix which is different from 1. The other method is to write the scattering matrix elements as polynomials in lambda, whose coefficients, though themselves functions of lamda, are uniformly bounded for lambda sufficiently small. The first order term in that expansion is the one given by perturbation theory. (Auth.)