Infrared analysis of quantum field theories

TL;DR

This paper demonstrates the stability of infrared solutions in multi-component $bbb4$ theories and extends the analysis to pure Yang-Mills, providing a method to map complex theories to scalar field spectra.

Contribution

It introduces a novel approach to analyze strongly coupled quantum field theories and extends it to multi-component and Yang-Mills theories.

Findings

Infrared solutions are stable in multi-component $bbb4$ theories.

The approach confirms the existence of asymptotic series in Yang-Mills theories.

Complex theories can be mapped to scalar field spectra in the infrared.

Abstract

We show that for a $\lambda\phi^4$ theory having many components, the solution with all equal components in the infrared regime is stable with respect to our expansion given by a recently devised approach to analyze strongly coupled quantum field theory. The analysis is extended to a pure Yang-Mills theory showing how, in this case, the given asymptotic series exists. In this way, many components theories in the infrared regime can be mapped to a single component scalar field theory obtaining their spectrum.