论文标题
Bererezin-toeplitz量化与较高的Bochner Laplacian相关的量
Berezin-Toeplitz quantization asssociated with higher Landau levels of the Bochner Laplacian
论文作者
论文摘要
在本文中，我们构建了一个紧凑型象征性歧管的Berezin-toeplitz类型量化。为此，我们选择了歧管上的riemannian度量，以便相关的bochner laplacian在每个点具有相同的局部模型（这比几乎是kähler量化的范围稍笼统）。 Then the spectrum of the Bochner Laplacian on high tensor powers $L^p$ of the prequantum line bundle $L$ asymptotically splits into clusters of size ${\mathcal O}(p^{3/4})$ around the points $pΛ$, where $Λ$ is an eigenvalue of the model operator (which can be naturally called a Landau level).我们使用量子空间开发了Toeplitz运算符演算，这是Bochner laplacian的特征空间，与Eigebvalues相对应。我们证明它提供了berezin-toeplitz量化。如果群集对应于多种多样水平，我们将获得toeplitz operators和正式的恒星产品的代数。对于最低的Landau级别，它恢复了几乎Kähler量化。
In this paper, we construct a family of Berezin-Toeplitz type quantizations of a compact symplectic manifold. For this, we choose a Riemannian metric on the manifold such that the associated Bochner Laplacian has the same local model at each point (this is slightly more general than in almost-Kähler quantization). Then the spectrum of the Bochner Laplacian on high tensor powers $L^p$ of the prequantum line bundle $L$ asymptotically splits into clusters of size ${\mathcal O}(p^{3/4})$ around the points $pΛ$, where $Λ$ is an eigenvalue of the model operator (which can be naturally called a Landau level). We develop the Toeplitz operator calculus with the quantum space, which is the eigenspace of the Bochner Laplacian corresponding to the eigebvalues frrom the cluster. We show that it provides a Berezin-Toeplitz quantization. If the cluster corresponds to a Landau level of multiplicity one, we obtain an algebra of Toeplitz operators and a formal star-product. For the lowest Landau level, it recovers the almost Kähler quantization.
