Probabilistic analysis of the ( q , 2)-Fock space: vacuum distribution and moments of the field operator

We study some probabilistic aspects of the (q,2)-Fock space over a given Hilbert space. Specifically, our focus is on determining the vacuum distribution of the field operator. We ascertain the precise expression for the vacuum expectation of any arbitrary product of creation and annihilation operators, with particular emphasis on the vacuum moments of the field operator. Utilizing these results, we calculate the moment-generating function of the field operator and subsequently determine the corresponding distribution.