几何量子化、复结构与相干态变换
Geometric quantization, complex structures and the coherent state transform
AI总结：
本文证明了紧致李群$K$的Hall相干态变换的热算子与$T^*K$上复结构族的厄米联络相关，并通过该联络的幺正平行移动确立了不同复结构下几何量子化的等价性，从而将李群相干态变换与Hitchin等人的结论相联系。
摘要：
本文证明了紧致李群$K$的Hall相干态变换中的热算子，与$T^*K$上自然单参数复结构族相关的厄米联络有关。该联络的幺正平行移动确立了在给定族内不同复结构选择下$T^*K$（几何）量子化的等价性。特别地，这些结果在李群的相干态变换与Hitchin及Axelrod、Della Pietra和Witten的结论之间建立了联系。
英文摘要：
It is shown that the heat operator in the Hall coherent state transform for a compact Lie group $K$ is related with a Hermitian connection associated to a natural one-parameter family of complex structures on $T^*K$. The unitary parallel transport of this connection establishes the equivalence of (geometric) quantizations of $T^*K$ for different choices of complex structures within the given family. In particular, these results establish a link between coherent state transforms for Lie groups and results of Hitchin and Axelrod, Della Pietra and Witten.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
