MODE-DEPENDENT FIELD RENORMALIZATION AND TRIVIALITY IN LAMBDA-PHI(4) THEORY

A continuum limit of the (lambda Phi(4))(4) theory exists which is ''t rivial'' (all scattering amplitudes vanish), but which does not corres pond to the zero-renormalized-coupling limit of conventional perturbat ion theory. This allows Spontaneous Symmetry Breaking and a very heavy , but still weakly interacting, Higgs boson. We answer some criticisms of this work, emphasizing that results from renormalization-group-imp roved perturbation theory are not valid. The phase transition encounte red as the bare mass-squared is made more and more negative is first o rder, contrary to the assumption of the conventional perturbative ''RG -improvement'' program.