Instantons in Large Order of the Perturbative Series

TL;DR

This paper investigates the large-order behavior of the Euclidean path integral in quantum models, revealing how instanton-anti-instanton pairs influence the divergence of perturbative series and connect to non-perturbative effects.

Contribution

It uncovers the role of instanton-anti-instanton pairs in the large-order perturbative series, extending understanding of non-perturbative contributions in quantum models.

Findings

Bounce configurations dominate at large order in models with tunneling.

A subleading peak at instanton-anti-instanton pairs reproduces the non-perturbative valley.

The perturbative series non-convergence is linked to these instanton effects.

Abstract

Behavior of the Euclidean path integral at large orders of the perturbation series is studied. When the model allows tunneling, the path-integral functional in the zero instanton sector is known to be dominated by bounce-like configurations at large order of the perturbative series, which causes non-convergence of the series. We find that in addition to this bounce the perturbative functional has a subleading peak at the instanton and anti-instanton pair, and its sum reproduces the non-perturbative valley.