$(q;l,\lambda)-$deformed Heisenberg algebra: representations, special functions and quantization
Mathematical Physics
2013-06-10 v2 math.MP
Abstract
This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements , derivedfrom deformed boson coherent states.The induced self-reproducing property with the associated self-reproducing kernel is computed and analyzed. An explicit construction of novel classes of generalized continuous Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.
Cite
@article{arxiv.1301.7028,
title = {$(q;l,\lambda)-$deformed Heisenberg algebra: representations, special functions and quantization},
author = {Mahouton Norbert Hounkonnou and Sama Arjika and Ezinvi Baloïtcha},
journal= {arXiv preprint arXiv:1301.7028},
year = {2013}
}