Large-Order Behavior of Perturbation Theory

Abstract

We examine the large-order behavior of perturbation theory for the anharmonic oscillator, a simple quantum-field-theory model. New analytical techniques are exhibited and used to derive formulas giving the precise rate of divergence of perturbation theory for all energy levels of the $x^{2N}$ oscillator. We compute higher-order corrections to these formulas for the $x^4$ oscillator with and without Wick ordering.