The Power of Perturbation Theory
Abstract
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the Picard-Lefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented.
Keywords
Cite
@article{arxiv.1702.04148,
title = {The Power of Perturbation Theory},
author = {Marco Serone and Gabriele Spada and Giovanni Villadoro},
journal= {arXiv preprint arXiv:1702.04148},
year = {2018}
}
Comments
v1: 42 pages, 8 figures; v2: 43 pages, 9 figures, minor improvements and references added, matches JHEP published version; v3: minor corrections and references added