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Holomorphic Hermite polynomials and a non-commutative plane
Gazeau J.-P., Hugon Szafraniec F.
Journal of Physics A: Mathematical and Theoretical 44 (2011) 495201 - http://hal.archives-ouvertes.fr/hal-00739312
Physique/Physique mathématique
Mathématiques/Physique mathématique
Holomorphic Hermite polynomials and a non-commutative plane
J.-P. Gazeau1, F. Hugon Szafraniec
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
http://www.apc.univ-paris7.fr/
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
France
APC - THEORIE
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.
Anglais

Journal of Physics A: Mathematical and Theoretical
Publisher Institute of Physics: Hybrid Open Access
ISSN 1751-8113 (eISSN : 1751-8121)
internationale
Articles dans des revues avec comité de lecture
12/2011
44
495201