标题： 关于$q$-变形的振子代数：$su_q(1,1)$和$su_q(2)$ 显示英文标题

标题： On the $q$-deformed oscillator algebras:$su_q(1,1)$ and $su_q(2)$

摘要： 我们研究单振子表示中$q$变形与$q$相干态之间的关系，针对$su_q(1,1)$和$su_q(2)$代数；以 Biedenharn、Macfarlane 和任意子振子形式的 Dyson 和 Holstein-Primakoff 类型。我们还讨论相关的 Fock-Bargmann$q$导数和积分。 显示英文摘要

摘要： We study the relations between $q$-deformations and $q$-coherent states of the single oscillator representations for $su_q(1,1)$ and $su_q(2)$ algebras; Dyson and Holstein-Primakoff type in terms of Biedenharn, Macfarlane and anyonic oscilators. We also discuss the related Fock-Bargmann $q$-derivative and integration.