Holomorphic Hermite polynomials and a non-commutative plane

J.-P. Gazeau 1 F. Hugon Szafraniec
1 APC - THEORIE
APC - UMR 7164 - AstroParticule et Cosmologie
Abstract : One more coherent state quantization of a complex plane is presented. Although the complex plane is equipped with a non-rotationally invariant measure, we still obtain a canonical commutation rule (up to a simple rescaling). We explain how the involved coherent states, built from holomorphic continuations of Hermite polynomials, are related to the non-commutative plane.
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Journal articles
Journal of Physics A: Mathematical and Theoretical, Institute of Physics: Hybrid Open Access, 2011, 44, pp.495201. <10.1088/1751-8113/44/49/495201>


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Submitted on : Sunday, October 7, 2012 - 7:05:59 PM
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J.-P. Gazeau, F. Hugon Szafraniec. Holomorphic Hermite polynomials and a non-commutative plane. Journal of Physics A: Mathematical and Theoretical, Institute of Physics: Hybrid Open Access, 2011, 44, pp.495201. <10.1088/1751-8113/44/49/495201>. <hal-00739312>

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