Triviality" and the Perturbative Expansion in $\lambda\Phi^4$ Theory
Abstract
The "triviality" of quantum field theory means that the renormalized coupling vanishes for infinite cutoff. That result inherently conflicts with the usual perturbative approach, which begins by postulating a non-zero, cutoff-independent . We show how a "trivial" solution 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 theory coupled to the Standard Model predicts a 2.2 TeV Higgs, but does NOT imply strong interactions in the scalar sector.
Cite
@article{arxiv.hep-ph/9403299,
title = {Triviality" and the Perturbative Expansion in $\lambda\Phi^4$ Theory},
author = {M. Consoli and P. M. Stevenson},
journal= {arXiv preprint arXiv:hep-ph/9403299},
year = {2007}
}
Comments
10 pages, LaTeX, no figures, DE-FG05-92ER40717-13, MAD/TH/94-4