A proposed "South-East rule" reads the directions of edges in a Borel-plane adjacency graph of critical values to decide, without steepest-descent flow computations, which complex and real saddles contribute to multidimensional oscillatory integrals.
The Power of Perturbation Theory
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
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.
representative citing papers
Renormalons can be understood as saddle points of the 1-loop effective action in toy models, enabled by the quantum scale anomaly.
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.
Presents explicit trans-series calculations for the double-well spectrum via exact WKB and path integral approaches up to four-instanton level.
citing papers explorer
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Which Saddles Contribute? The South-East Rule for Multidimensional Integrals
A proposed "South-East rule" reads the directions of edges in a Borel-plane adjacency graph of critical values to decide, without steepest-descent flow computations, which complex and real saddles contribute to multidimensional oscillatory integrals.
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Renormalons as Saddle Points
Renormalons can be understood as saddle points of the 1-loop effective action in toy models, enabled by the quantum scale anomaly.
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Lectures on Semiclassical Methods for Composite Operators
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.
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The Double Well Done Doubly-Well
Presents explicit trans-series calculations for the double-well spectrum via exact WKB and path integral approaches up to four-instanton level.