Holomorphic Hermite polynomials and a non-commutative plane

J.-P. Gazeau , 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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

J.-P. Gazeau, F. Hugon Szafraniec. Holomorphic Hermite polynomials and a non-commutative plane. Journal of Physics A: Mathematical and Theoretical, 2011, 44, pp.495201. ⟨10.1088/1751-8113/44/49/495201⟩. ⟨hal-00739312⟩