The Power of Perturbation Theory. Serone, M., Spada, G., & Villadoro, G. , 2, 2017. Paper doi abstract bibtex 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.
@article{Serone-2017-ID296,
title = {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.},
author = {Serone, Marco and Spada, Gabriele and Villadoro, Giovanni},
journal = {},
year = {2017},
month = {2},
url = {http://arxiv.org/abs/1702.04148v2},
url = {http://arxiv.org/pdf/1702.04148v2},
arxiv = {1702.04148v2},
doi = {10.1007/JHEP05(2017)056},
keywords = {hep-th},
file = {FULLTEXT:pdfs/000/000/000000296.pdf:PDF}
}
Downloads: 0
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