Strongly coupled quantum field theory

TL;DR

This paper demonstrates that in a strongly coupled 2D λφ^4 theory, homogeneous solutions dominate time evolution, enabling a Green function approach and revealing a harmonic oscillator mass spectrum consistent with perturbation theory.

Contribution

It introduces a numerical analysis showing homogeneous solutions dominate in strong coupling, allowing Green function methods and deriving a harmonic oscillator spectrum in a non-linear quantum field theory.

Findings

Homogeneous solutions dominate at strong coupling.

Green function method is applicable in this regime.

Mass spectrum matches that of a harmonic oscillator.

Abstract

We analyze numerically a two-dimensional $\lambda\phi^4$ theory showing that in the limit of a strong coupling $\lambda\to\infty$ just the homogeneous solutions for time evolution are relevant in agreement with the duality principle in perturbation theory as presented in [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], being negligible the contribution of the spatial varying parts of the dynamical equations. A consequence is that the Green function method works for this non-linear problem in the large coupling limit as in a linear theory. A numerical proof is given for this. With these results at hand, we built a strongly coupled quantum field theory for a $\lambda\phi^4$ interacting field computing the first order correction to the generating functional. Mass spectrum of the theory is obtained turning out to be that of a harmonic oscillator with no dependence on the dimensionality of spacetime. The agreement with the Lehmann-K\"allen representation of the perturbation series is then shown at the first order.