论文标题
精确WKB分析的捆绑量化
Sheaf quantization from exact WKB analysis
论文作者
论文摘要
捆绑量化是与拉格朗日河畔的捆绑关系。通过使用精确的WKB分析的结果，我们在对Stokes曲线行为的某些假设下将光谱曲线在Novikov环上进行了分解。对于Schrödinger方程，我们证明，可以通过Voros-Iwaki-Nakanishi坐标识别与光谱曲线相关的局部系统。我们预计这些捆绑量化是$ \ hbar $增强的Riemann-Hilbert通信的对象级实现。
A sheaf quantization is a sheaf associated to a Lagrangian brane. By using the results of exact WKB analysis, we sheaf-quantize spectral curves over the Novikov ring under some assumptions on the behavior of Stokes curves. For Schrödinger equations, we prove that the local system associated to the sheaf quantization (microlocalization a.k.a. abelianization) over the spectral curve can be identified with the Voros--Iwaki--Nakanishi coordinate. We expect that these sheaf quantizations are the object-level realizations of the $\hbar$-enhanced Riemann--Hilbert correspondence.
