Dual perturbation expansion for a classical $\lambda {\varphi }^4$ field theory

Abstract

We prove the existence of a strong coupling expansion for a classical $\lambda {\varphi }^4$ 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.

Comments: 7 pages, no figures. Version accepted for publication in International Journal of Modern Physics A