Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 12, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP12(2020)114
Keywords
Nonperturbative Effects; Resummation; Solitons Monopoles and Instantons
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Funding
- Japan Society for the Promotion of Science (JSPS) [18H01217, 19K03817]
- U.S. Department of Energy, Office of Science, Office of Nuclear Physics [DE-FG02-03ER41260]
- Grants-in-Aid for Scientific Research [19K03817] Funding Source: KAKEN
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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 Schrodinger 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's 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.
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