Proof of triviality of $λϕ^4$ theory

Abstract

We show that a recent analysis in the strong coupling limit of the $λϕ^4$ 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.

5 pages, 1 figure. Updated references and added some more. Comparison with lattice data of the gluon propagator is given finding excellent agreement. Accepted for publication in International Journal of Modern Physics A