Infrared behavior of the running coupling in scalar field theory
Abstract
We compute the Green function of the massless scalar field theory in the infrared till the next-to-leading order, providing a fully covariant strong coupling expansion. Applying Callan-Symanzik equation we obtain the exact running coupling for this case by computing the beta function. This result is applied using a recently proved mapping theorem between a massless scalar field theory and Yang-Mills theory. This beta function gives a running coupling going to zero as in agreement with lattice results presented in Boucaud et al. [JHEP 0304 (2003) 005] and showing that the right definition of the running coupling for a Yang-Mills theory in the infrared is given in a MOM scheme. The emerging scenario is supporting a quantum field theory based on instantons.
Keywords
Cite
@article{arxiv.0802.1183,
title = {Infrared behavior of the running coupling in scalar field theory},
author = {Marco Frasca},
journal= {arXiv preprint arXiv:0802.1183},
year = {2015}
}
Comments
19 pages, 2 figures. Completely revised version introducing for the first time a covariant version of our strong coupling expansion in quantum field theory