Two-boson realizations of the Higgs algebra and some applications

Abstract

In this paper two kinds of two-boson realizations of the Higgs algebra are obtained by generalizing the well known Jordan-Schwinger realizations of the SU(2) and SU(1,1) algebras. In each kind, an unitary realization and two nonunitary realizations, together with the properties of their respective acting spaces are discussed in detail. Furthermore, similarity transformations, which connect the nonunitary realizations with the unitary ones, are gained by solving the corresponding unitarization equations. As applications, the dynamical symmetry of the Kepler system in a two-dimensional curved space is studied and the phase operators of the Higgs algebra is constructed.