On the combinatorics of normal ordering bosonic operators and deformations of it

Abstract

Recently some combinatorial aspects for the normal ordering of powers of arbitrary monomials of boson operators were discussed. In particular, it was shown that the resulting formulae lead to generalizations of the usual Bell and Stirling numbers. In this paper these considerations are generalized to the q-deformed case. In particular, it is shown that the simplest example of this generalization leads to q-deformed Lah numbers. The connection between (generalized) Stirling and Bell numbers and matrix elements of the above-mentioned operators with respect to the usual Fock space basis and coherent states is discussed.