Groupoids and Geometric Quantization

经典力学和量子力学的数学模型是非常不同的。事实上，经典力学描述了大尺度上的物理定律（例如摆动的钟摆，行星轨道等的运动定律），并且在数学上根植于微分几何，微分几何是微积分的延伸，适用于更一般的空间，允许曲率和更高的维度。相比之下，量子力学描述的是亚原子尺度上的物理定律，它植根于人类的语言

The mathematical models underlying classical mechanics and quantum mechanics are very different. Indeed, classical mechanics describes physical laws on a large scale (e.g. laws of motion for a swinging pendulum, planetary orbits, etc.) and is mathematically rooted in differential geometry, an extension of calculus to more general spaces that allow for curvature and higher dimensions. In contrast, quantum mechanics describes the physical laws on a subatomic scale and is rooted in the language of