Geometric quantization, complex structures and the coherent state transform

Carlos Florentino; Pedro Matias; Jose Mourao; Joao P. Nunes

doi:10.1016/j.jfa.2004.10.021

Geometric quantization, complex structures and the coherent state transform

微分几何 2023-09-11 v2 高能物理 - 理论数学物理泛函分析 math.MP

作者: Carlos Florentino , Pedro Matias , Jose Mourao , Joao P. Nunes

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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.

关键词

algebraic k-theory quantum groups lie groups

引用

@article{arxiv.math/0402313,
  title  = {Geometric quantization, complex structures and the coherent state transform},
  author = {Carlos Florentino and Pedro Matias and Jose Mourao and Joao P. Nunes},
  journal= {arXiv preprint arXiv:math/0402313},
  year   = {2023}
}

备注

to appear in Journal of Functional Analysis

Geometric quantization, complex structures and the coherent state transform

摘要

关键词

引用

备注

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