多项式角动量代数的代数表示及实现

Algebraic representations of polynomial angular momentum algebra and Its realizations

本文利用三参数李群求代数表示的方法求出多项式角动量代数的代数表示及其酉表示,找到一个能同时承载李代数及相对应的多项式角动量代数的基底,并在该基底下求出两种代数之间的联系,利用该联系则也可求出多项式角动量代数的代数表示.最后求出多项式角动量代数的单玻色实现及其在有限维多项式函数空间的微分实现.

At first the representations of polynomial angular momentum algebra and its unitary ones are obtained appling the way to get the three-parameter Lie algebra representations. Then find the basis which can be acted on by both Lie algebra and the polynomial angular momentum algebra simultaneity, so under such basis the representations of deformed algebras can be shown by introducing the relation of two algebra. At last the deformed algebra＇s single boson operator realization and one differential realization under finite-dimensional spaces are deduced.