On $(alpha, q)$-Poisson Operators and Their Distributions (Mathematical aspects of quantum fields and related topics)

Abstract

We propose an (α, q)-analogue of the Poisson operator on the Fock space of Bożejko-Ejsmont-Hasebe [6] and discuss a probability law of the operator. We show that the probability law is expressed by the q-Meixner distribution. Our results contain not only symmetric distributions as in [6], but also non-symmetric ones such as free Poisson, q and q²- deformations of Poisson, Pascal, Gamma, and Meixner distributions. This is the summary of the paper [4].