LANDAU POLES, ULTRAVIOLET FIXED-POINTS, AND TRIVIALITY IN THE PERTURBATIVE EXPANSION OF (LAMBDA-PHI(4))(4)

The ''triviality'' of (lambda Phi(4))(4) means that the continuum theo ry has a vanishing renormalized coupling lambda(R). This result inhere ntly conflicts with the standard perturbative approach, which begins b y postulating a nonzero, cutoff-independent lambda(R), and which suffe rs from pathologies - either Landau poles (in odd orders) or spurious ultraviolet fixed points (in even orders). We show how the known struc ture of perturbation theory can be rearranged, to arbitrarily high ord ers, to fulfil the condition lambda(R) = 0. The corresponding renormal ization group flow of the bare coupling coincides with that needed to renormalize the effective potential. as calculated in any ''triviality ''-compatible approximation. Although lambda(R) vanishes, the physical mass is finite; there is no proportionality between the two. That imp lies that the Higgs mass does not represent a measure of the observabl e interaction strength in the scalar sector of the standard model.