布洛赫理论与磁系统的量子化
Bloch Theory and Quantization of Magnetic Systems
摘要：
在有磁场的黎曼流形上量子化粒子的运动，提出了量子化的存在性和唯一性问题。这两个问题在几何量子化的早期就已经解决了，但仍然有一些结构上的见解需要从谱理论中获得。继Asch，Over & Seiler（1994）对2-torus的工作之后，我们描述了更一般的紧流形上流形上的量子化与其覆盖空间上的Bloch理论之间的关系。
英文摘要：
Quantizing the motion of particles on a Riemannian manifold in the presence of a magnetic field poses the problems of existence and uniqueness of quantizations. Both of them are settled since the early days of geometric quantization but there is still some structural insight to gain from spectral theory. Following the work of Asch, Over & Seiler (1994) for the 2-torus we describe the relation between quantization on the manifold and Bloch theory on its covering space for more general compact manifolds.
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