3 years ago

The Power of Perturbation Theory.

Giovanni Villadoro, Marco Serone, Gabriele Spada

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.

Publisher URL: http://arxiv.org/abs/1702.04148

DOI: arXiv:1702.04148v3

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