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Convergence of the Wick star product. (English) Zbl 1203.53089
Summary: We construct a Fréchet space as a subspace of \({C^\omega(\mathbb{C}^n)}\) where the Wick star product converges and is continuous. The resulting Fréchet algebra \({\mathcal{A}}_\hbar\) is studied in detail including a \(^{*}\)-representation of \({\mathcal{A}}_\hbar\) in the Bargmann-Fock space and a discussion of star exponentials and coherent states.

MSC:
53D55 Deformation quantization, star products
46L65 Quantizations, deformations for selfadjoint operator algebras
81R30 Coherent states
81S10 Geometry and quantization, symplectic methods
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