Triviality" and the Perturbative Expansion in $λΦ^4$ Theory

Abstract

The "triviality" of $(λΦ^4)_4$ quantum field theory means that the renormalized coupling $λ_R$ vanishes for infinite cutoff. That result inherently conflicts with the usual perturbative approach, which begins by postulating a non-zero, cutoff-independent $λ_R$. We show how a "trivial" solution $λ_R=0$ can be compatible with the known structure of perturbation theory to arbitrarily high orders, by a simple re-arrangement of the expansion. The "trivial" solution reproduces the result obtained by non-perturbative renormalization of the effective potential. The physical mass is finite, while the renormalized coupling strength vanishes: the two are NOT proportional. The classically scale-invariant $λΦ^4$ theory coupled to the Standard Model predicts a 2.2 TeV Higgs, but does NOT imply strong interactions in the scalar sector.