SINGLE BOSON AND INVERSION BOSON REALIZATIONS OF MULTI-PARAMETER NONLINEARLY DEFORMED ANGULAR MOMENTUM ALGEBRA

Abstract

Explicit, analytic and closed expressions for boson realizations of the (m+3)-parameter nonlinearly deformed angular momentum algebra [Formula: see text] with its highest power m of polynomial function being arbitrary, which combines and generalizes Witten's two deformation schemes, are investigated in terms of the single boson and the single inversion boson, respectively. For each kind, the unitary Holstein–Primakoff-like realization, the non-unitary Dyson–Maléev-like realization and their connections are respectively discussed. Using these realizations, the corresponding representations of [Formula: see text] as well as their respective acting spaces in the Fock space are obtained.