Abstract
In this paper two kinds of two-boson realizations of the polynomial angular momentum algebra are obtained by generalizing the well known Jordan–Schwinger realizations of the SU(2) and SU(1,1) algebras. Especially, for the Higgs algebra, 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 phase operators of the Higgs algebra are constructed.
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