论文标题
自由粒子的复杂几何形状及其扰动
The complex geometry of the free particle, and its perturbations
论文作者
论文摘要
在路径上描述量子粒子的汉密尔顿操作员通常会塑性地延伸到路径的复杂邻域。当这样做时，它可以看作是复杂的投影结构的局部表达，其扰动成为该几何结构的变形。我们将将自由粒子的哈密顿量描述为一个复杂的投影表面，我们将使用清单几何形状中的工具来研究其扰动。我们的主要结果是基于代数“转化理论”的结果宽松建模的，该结果是确切的WKB方法。它们是为了获得对确切的WKB方法的几何理解的努力的基础。
The Hamiltonian operator describing a quantum particle on a path often extends holomorphically to a complex neighborhood of the path. When it does, it can be seen as the local expression of a complex projective structure, and its perturbations become deformations of that geometric structure. We'll describe the Hamiltonian of a free particle as a complex projective surface, and we'll use tools from quasiconformal geometry to study its perturbations. Our main results are loosely modeled on the algebraic "transformation theory" results that underpin the exact WKB method. They're meant to serve as a foundation for efforts to gain a more geometric understanding of the exact WKB method.
