Generating Non-perturbative Physics from Perturbation Theory

TL;DR

This paper demonstrates that in quantum systems, the complete non-perturbative energy spectrum can be derived solely from perturbative expansions and boundary conditions, exemplifying the resurgence principle and extending to some quantum field theories.

Contribution

It shows how to generate full non-perturbative energy expressions from perturbation theory combined with boundary conditions, illustrating resurgence in quantum mechanics and field theory.

Findings

Full non-perturbative energies derived from perturbation series

Resurgence relates fluctuations around different saddle points

Method applicable to certain quantum field theories

Abstract

In a large variety of quantum mechanical systems, we show that the full non-perturbative expression for energy eigenvalues, containing all orders of perturbative, non-perturbative and quasi-zero-mode terms, may be generated directly from the perturbative expansion about the perturbative vacuum, combined with a single global boundary condition. This provides a dramatic realization of the principle of "resurgence", that the fluctuations about different semiclassical saddle points are related to one another in a precise quantitative manner. The analysis of quantum mechanics also generalizes to certain calculable regimes of quantum field theory.