Dual perturbation expansion for a classical $\lambda\phi^4$ field theory

TL;DR

This paper establishes a strong coupling expansion for a classical  field theory, demonstrating the duality principle and showing how corrections renormalize the leading snoidal wave solution.

Contribution

It introduces a dual perturbation expansion for  theory, providing explicit solutions and corrections that align with the duality principle in perturbation theory.

Findings

Existence of a strong coupling expansion proven.

Leading order solution is a snoidal wave, replacing free theory plane waves.

Higher order corrections renormalize the leading solution.

Abstract

We prove the existence of a strong coupling expansion for a classical $\lambda\phi^4$ field theory in agreement with the duality principle in perturbation theory put forward in [M.Frasca, Phys. Rev. A 58, 3439 (1998)]. The leading order solution is a snoidal wave taking the place of plane waves of the free theory. We compute the first order correction and show that higher order terms do renormalize the leading order solution.