Quantum potential with no perturbative series, and nonperturbative vacuum dominated by complex classical paths

TL;DR

This paper introduces a potential with no perturbative series, where nonperturbative vacuum energy is derived from complex classical paths, challenging traditional perturbative approaches.

Contribution

It presents a potential where perturbative series are entirely absent, and nonperturbative effects are captured by complex classical solutions.

Findings

Perturbative series are completely absent in the proposed potential.

Nonperturbative vacuum energy is computed from complex classical paths.

The approach challenges the reliance on perturbative series in quantum potentials.

Abstract

Spectra of standard 1d potentials (double-well, sin-Gordon etc) are given by trans-series in coupling, including (badly divergent) perturbative series (PS), and nonperturbative terms. All of them are badly defined (e.g. PS are badly divergent) but in sum supposed to be good. In this paper we discuss an example of a potential with specially defined couplings making PS completely absent. We calculate its nonperturbative vacuum energy and show that they are reproduced by the action of certain complex solutions to holomorphic Newton equation.