Algebraic structure of the Lie algebra<i>so</i>(2,1) for a quantized field in a vibrating cavity
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Abstract
It is shown that the generators of the Lie algebra so(2,1) can be defined in terms of annihilation and creation operators of infinite boson modes while an angular momentum algebra can be introduced with finite boson modes. The so(2,1) algebraic structure is shown to exist in the quantized field in a vibrating cavity, which considerably simplifies the studies on the system's eigenvalue problem and the dynamical evolution.
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