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

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

2011-01-02

arxiv.org/abs/1101.0379v3

Mathematics

Complex Variables

13 pages

Scientific paper

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.

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