On exact-WKB analysis, resurgent structure, and quantization conditions
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Publication:2660255
DOI10.1007/JHEP12(2020)114zbMATH Open1457.81048arXiv2008.00379OpenAlexW3114353274MaRDI QIDQ2660255
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Publication date: 29 March 2021
Published in: (Search for Journal in Brave)
Abstract: There are two well-known approaches to studying nonperturbative aspects of quantum mechanical systems: Saddle point analysis of the partition functions in Euclidean path integral formulation and the exact-WKB analysis based on the wave functions in the Schr"{o}dinger equation. In this work, based on the quantization conditions obtained from the exact-WKB method, we determine the relations between the two formalism and in particular show how the two Stokes phenomena are connected to each other: the Stokes phenomenon leading to the ambiguous contribution of different sectors of the path integral formulation corresponds to the change of the "topology" of the Stoke curves in the exact-WKB analysis. We also clarify the equivalence of different quantization conditions including Bohr-Sommerfeld, path integral and Gutzwiller's ones. In particular, by reorganizing the exact quantization condition, we improve Gutzwiller analysis in a crucial way by bion contributions (incorporating complex periodic paths) and turn it into an exact result. Furthermore, we argue the novel meaning of quasi-moduli integral and provide a relation between the Maslov index and the intersection number of Lefschetz thimbles.
Full work available at URL: https://arxiv.org/abs/2008.00379
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