Geometric Quantization, Complex Structures and the Coherent State Transform
نویسندگان
چکیده
It is shown that the heat operator in the Hall coherent state transform for a compact Lie group K [Ha1] 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 [Hi] and Axelrod, Della Pietra and Witten [AdPW].
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