Geometric quantization, complex structures and the coherent state transform
نویسندگان
چکیده
منابع مشابه
Geometric Quantization, Complex Structures and the Coherent State Transform
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 fa...
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It is shown here and in the preceeding paper [1] that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of genera...
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In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systematic treatment of the construction of such systems and to collect some recent results. We begin by recalling the basic constructions of geometric quantization in both the Kähler and non-Kähler cases. We then study the re...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2005
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2004.10.021