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

Edward Shuryak*

  • Center for Nuclear Theory, Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794–3800, USA

  • *Contact author: edward.shuryak@stonybrook.edu
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Phys. Rev. D 114, 085015 – Published 20 October, 2026

DOI: https://doi.org/10.1103/wcpr-hvfw

Abstract

Spectra of standard one-dimensional potentials (double-well, sin-Gordon, etc.) are given by trans-series in coupling, including (badly divergent) perturbative series and nonperturbative terms ∼exp(−const/g2) and log(1/g)exp(−const/g2). All of them are badly defined (e.g., perturbative series 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 perturbative series completely absent. We calculate its nonperturbative vacuum energy and show that they are reproduced by the action of certain complex solutions to the holomorphic Newton equation.

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Phys. Rev. D 114, 085015– Published 20 October, 2026
  • Received 4 June 2026
  • Accepted 6 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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