On the Breakdown of Perturbation Theory

TL;DR

This paper discusses the limitations of perturbation theory in weakly-coupled theories, exploring non-perturbative effects and the potential for semiclassical estimates of particle production and tunneling phenomena.

Contribution

It analyzes the breakdown of perturbation theory and evaluates the prospects of rigorous and semiclassical estimates for non-perturbative particle production.

Findings

Perturbation theory fails to account for certain non-perturbative particle production.

Induced tunneling can be exponentially enhanced at specific frequencies.

Large-order behavior of Green functions reveals insights into non-perturbative effects.

Abstract

The production of o(1/g^2) particles in a weakly-coupled theory is believed to be non-perturbatively suppressed. I comment on the prospects of (a) establishing this rigorously, and (b) estimating the effect to exponential accuracy semiclassically, by discussing two closely-related problems: the large-order behaviour of few-point Green functions, and induced excitation in quantum mechanics. Induced tunneling in the latter case is exponentially enhanced for frequencies of the order of the barrier height.