Infrared analysis of quantum field theories

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.