Two-boson Realizations of the Polynomial Angular Momentum Algebra and Some Applications |
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| Authors: | Dong Ruan |
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| Institution: | (1) Department of Physics and Key Laboratory for Quantum Information and Measurements of Ministry of Education, Tsinghua University, Beijing, 100084, China;(2) Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou, 730000, China |
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| 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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| Keywords: | polynomial angular momentum algebra Higgs algebra boson realization Kepler system phase operator |
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