Coherent States Quantization for Generalized Bargmann Spaces with Formulae for their Attached Berezin Transforms in Terms of the Laplacian on Cn

2011/01/02 by Zouhaı̈r Mouayn, Zouhair Mouayn, Mouayn, Zouhair
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.CV #math.MP

paper · pdf · doi:10.48550/arxiv.1101.0379

13 pages

openalex publication_date 2011/01/02 · arxiv created 2011/10/02 · arxiv updated 2011/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

While dealing with a class of generalized Bargmann spaces, we rederive their reproducing kernels from the knowledge of an orthonormal basis by using an addition formula for Laguerre polynomials involving the disk polynomials. We construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover the Berezin transforms attached to these spaces. Finally, two new formulae representing these transforms as functions of the Euclidean Laplacian are established and a possible physics direction for the application of such formulae is discussed.

Citations

• A formula representing Magnetic Berezin Transformsas functions of the Laplacian on Cn

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