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Beiser, Svea; Römer, Hartmann; Waldmann, Stefan

Convergence of the Wick star product. (English) Zbl 1203.53089

Commun. Math. Phys. 272, No. 1, 25-52 (2007).
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.

Cited in 13 Documents

MSC:

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

Keywords:

Fréchet space; Wick star product; Bargmann-Fock space; star exponentials; coherent states
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\textit{S. Beiser} et al., Commun. Math. Phys. 272, No. 1, 25--52 (2007; Zbl 1203.53089)
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