Boson realizations of the polynomial angular momentum algebras with arbitrary powers and their unitarization

Abstract

The inhomogeneous single-, two- and three-boson realizations of the more general polynomial angular momentum algebra SU Λ(2) are obtained from the Fock representations of SU Λ(2) that correspond to the indecomposable representation on the space of universal enveloping algebra U( SU Λ(2)) and to the induced representations on the quotient spaces U( SU Λ(2))/I i , with I i being some left ideals with respect to U( SU Λ(2)) . Then these boson realizations are unitarized by the corresponding similarity transformations. As examples, the explicit expressions for the similarity transformations used to unitarize the inhomogeneous single-boson realizations of SU 2(2) and the Higgs algebra are respectively calculated.