Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 5, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP05(2017)056
Keywords
Nonperturbative Effects; Field Theories in Lower Dimensions; Resummation
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Funding
- ERC [267985]
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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.
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