Proof of triviality of $\lambda\phi^4$ theory

TL;DR

This paper demonstrates that in the strong coupling limit, the $bb\u03bclambdabphi^4$ theory becomes trivial, effectively reducing to a free quantum field theory with a harmonic oscillator spectrum.

Contribution

It provides a rigorous proof that the $bbbclambdabphi^4$ theory is trivial in the strong coupling limit, including explicit expressions for the propagator and renormalized parameters.

Findings

The theory reduces to a free quantum field theory in the strong coupling limit.

The spectrum matches that of a harmonic oscillator.

Comments on the triviality of Yang-Mills theory in the infrared are included.

Abstract

We show that a recent analysis in the strong coupling limit of the $\lambda\phi^4$ theory proves that this theory is indeed trivial giving in this limit the expansion of a free quantum field theory. We can get in this way the propagator with the renormalization constant and the renormalized mass. As expected the theory in this limit has the same spectrum as a harmonic oscillator. Some comments about triviality of the Yang-Mills theory in the infrared are also given.