几何量子化中的谱收敛--非ingular Langrangian fibrations的情况

IF 0.6 3区 数学 Q3 MATHEMATICS
Kota Hattori, Mayuko Yamashita
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引用次数: 0

摘要

本文是 $\href{https://dx.doi.org/10.4310/JSG.2020.v18.n6.a3}{[11]}$ 的续篇。我们利用度量空间的收敛理论开发了一种几何量化的新方法。给定在预量化交点流形上收敛于非星实极化的凯勒极化族,我们展示了 $\overline{\partial}$-Laplacians 的谱收敛结果,以及量子希尔伯特空间的收敛结果。我们还考虑了相容近复结构的近凯勒量化情况,并展示了类似的收敛结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Spectral convergence in geometric quantization — the case of non-singular Langrangian fibrations
This paper is a sequel to $\href{https://dx.doi.org/10.4310/JSG.2020.v18.n6.a3}{[11]}$. We develop a new approach to geometric quantization using the theory of convergence of metric measure spaces. Given a family of Kähler polarizations converging to a non-singular real polarization on a prequantized symplectic manifold, we show the spectral convergence result of $\overline{\partial}$-Laplacians, as well as the convergence result of quantum Hilbert spaces. We also consider the case of almost Kähler quantization for compatible almost complex structures, and show the analogous convergence results.
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.
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