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

Phillial Oh; Chaiho Rim

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

Phillial Oh·Chaiho Rim

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Abstract

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.

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Phillial Oh, Chaiho Rim. 1996-09-10. On the $q$-deformed oscillator algebras:$su_q(1,1)$ and $su_q(2)$. https://arxiv.org/abs/q-alg/9609009

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