Note on weighted $q$-Fock spaces and $q$-orthogonal polynomials (Mathematical aspects of quantum fields and related topics)

Abstract

In this short note, we shall discuss weighted $q$-Fock spaces, field operators and their vacuum distributions, which have strong connections with $q$-orthogonal polynomials including discrete $q$-Hermite I polynomials. One can see that our general approach can treat not only known examples scattered in [1][5][8][9][10][13], but also can involve non-trivial and interesting examples, which were not referred in previous works [5][11]. This is a summary paper of our paper [4].