论文标题
兰道水平紧凑
Landau levels on a compact manifold
论文作者
论文摘要
我们在紧凑的歧管上考虑具有恒定的非分级磁场的磁性laplacian。在较大的场限制中，众所周知，特征值分组为簇，相应的特征空间总和称为兰道水平。一级已被深入研究，作为Kaehler量化的自然概括。当前的论文专门用于较高的水平：我们计算它们的尺寸为Riemann-Roch数字，研究相关的Toeplitz代数，并证明每个级别都是同构的，并通过方便的辅助束扭曲了量化。
We consider a magnetic Laplacian on a compact manifold, with a constant non-degenerate magnetic field. In the large field limit, it is known that the eigenvalues are grouped in clusters, the corresponding sums of eigenspaces being called the Landau levels. The first level has been studied in-depth as a natural generalization of the Kaehler quantization. The current paper is devoted to the higher levels: we compute their dimensions as Riemann-Roch numbers, study the associated Toeplitz algebras and prove that each level is isomorphic with a quantization twisted by a convenient auxiliary bundle.
