2020/08/31 by Naohisa Sueishi, Syo Kamata, Tatsuhiro Misumi +1
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep12(2020)114
published as JHEP 12 (2020) 114 · 51 pages, 12 figures, typo corrected, added comments into Sec.IV
arxiv created 2020/10/16 · arxiv updated 2021/01/01
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 Schrödinger 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.