Generating Non-perturbative Physics from Perturbation Theory

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.

5 pages; 2 figures; published version in PRD

References in corpus (8)

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• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
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