Higgs代数的双玻色子实现及其应用
Two-boson realizations of the Higgs algebra and some applications
摘要：
本文通过推广SU（2）和SU（1，1）代数的Jordan-Schwinger实现，得到了Higgs代数的两种两玻色子实现.在每一类中，我们详细讨论了一个酉实现和两个非酉实现，以及它们各自作用空间的性质。通过求解相应的酉化方程，得到了连接非酉实现与酉实现的相似变换。作为应用，研究了二维弯曲空间中Kepler系统的动力学对称性，构造了Higgs代数的相算符。
英文摘要：
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.
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