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Some comments on $q$-deformed oscillators and $q$-deformed $su(2)$ algebras

L. C. Kwek·C. H. Oh
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Abstract

The various relations between $q$-deformed oscillators algebras and the $q$-deformed $su(2)$ algebras are discussed. In particular, we exhibit the similarity of the $q$-deformed $su(2)$ algebra obtained from $q$-oscillators via Schwinger construction and those obtained from $q$-Holstein-Primakoff transformation and show how the relation between $su_{\sqrt{q}}(2)$ and Hong Yan $q$-oscillator can be regarded as an special case of Inöuë- Wigner contraction. This latter observation and the imposition of positive norm requirement suggest that Hong-Yan $q$-oscillator algebra is different from the usual $su_{\sqrt{q}}(2)$ algebra, contrary to current belief in the literature.

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BibTeXRIS

L. C. Kwek, C. H. Oh. 1997-12-16. Some comments on $q$-deformed oscillators and $q$-deformed $su(2)$ algebras. https://doi.org/10.1007/s100529800816

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