论文标题
关于精确的WKB分析，复兴结构和量化条件
On exact-WKB analysis, resurgent structure, and quantization conditions
论文作者
论文摘要
研究了量子机械系统的非扰动方面的两种知名方法：欧几里得路径积分配方中分区函数的鞍点分析和基于Schrödinger方程中波函数的精确WKB分析。在这项工作中，基于从确切的WKB方法获得的量化条件，我们确定了两种形式主义之间的关系，特别是表明了两种stokes现象如何相互联系：Stokes现象导致路径积分配方的不同阶层的含糊贡献与确切的Stoke Curves分析的“拓扑”的变化相对应。 我们还阐明了不同量化条件的等效性，包括Bohr-Sommerfeld，Path Intemall和Gutzwiller的等效性。特别是，通过重新组织确切的量化条件，我们通过Bion贡献（结合复杂的周期性路径）以至关重要的方式改善了Gutzwiller分析，并将其转变为确切的结果。此外，我们争论了准穆多利积分的新颖含义，并提供了Maslov指数与Lefschetz Thimbles的交点之间的关系。
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.
