English

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

High Energy Physics - Theory 2026-05-13 v2

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.

Keywords

Cite

@article{arxiv.2603.14467,
  title  = {Quantum potential with no perturbative series, and nonperturbative vacuum dominated by complex classical paths},
  author = {Edward Shuryak},
  journal= {arXiv preprint arXiv:2603.14467},
  year   = {2026}
}

Comments

version 2 contains new section about convergence of Hamiltonian renormalization group for this potential

R2 v1 2026-07-01T11:20:50.787Z