Instantons from Perturbation Theory

TL;DR

This paper demonstrates how non-perturbative effects like instantons can be incorporated into modified perturbative series in quantum mechanics, providing a way to obtain exact results from perturbation theory.

Contribution

It introduces a method to encode full non-perturbative results within a modified perturbative framework for certain quantum mechanical systems.

Findings

Non-perturbative effects can be captured by modified perturbative series.

Explicit examples include the double-well potential and anharmonic oscillator.

The approach reproduces exact results in systems with known non-perturbative contributions.

Abstract

In quantum mechanics and quantum field theory perturbation theory generically requires the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results. We show how full non-perturbative results can be encoded in a suitable modified perturbative series in a class of quantum mechanical problems. We illustrate this explicitly in examples which are known to contain non-perturbative effects, such as the (supersymmetric) double-well potential, the pure anharmonic oscillator, and the perturbative expansion around a false vacuum.