Harmonic oscillator realization of the deformed Bogoliubov (p, q)-transformations without first finite Fock states

Abstract

Considering a simple generalization of the (p, q)-deformed boson oscillator algebra, which leads to a two-parameter deformed bosonic algebra in an infinite dimensional subspace of the harmonic oscillator Hilbert space without first finite Fock states, we establish a new harmonic oscillator realization of the deformed boson operators based on the Bogoliubov (p, q)-transformations. We obtain exact expressions for the transformation coefficients and show that they depend on arbitrary functions of p and q which can be interpreted as the parameters of the (p, q)-deformed GL(2, C) group. We also examine the existence and structure of the corresponding deformed Fock-space representation for our problem.