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Journal of Physics A: Mathematical and Theoretical 44 (2011) 495201
Holomorphic Hermite polynomials and a non-commutative plane
J.-P. Gazeau1, F. Hugon Szafraniec

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.
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
Physique/Physique mathématique

Mathématiques/Physique mathématique