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.
Real-Time Feynman Path Integral Realization of Instantons
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abstract
In Euclidean path integrals, quantum mechanical tunneling amplitudes are associated with instanton configurations. We explain how tunneling amplitudes are encoded in real-time Feynman path integrals. The essential steps are borrowed from Picard-Lefschetz theory and resurgence theory.
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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.