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The European Physical Journal C
ISSN: 1434-6044 (printed version)
ISSN: 1434-6052 (electronic version)
Abstract Volume 5 Issue 1 (1998) pp 189-193
DOI 10.1007/s100529800816
theoretical physics:
Some comments on $q$-deformed oscillators and $q$-deformed $su(2)$ algebras
L.C. Kwek, C.H. Oh
Department of Physics, Faculty of Science, National University of Singapore, Lower Kent Ridge, Singapore 119260, Republic of Singapore (e-mail: scip6051@leonis.nus.edu.sg, phyohch@leonis.nus.edu.sg)
Received: 21 July 1997 / Revised version: 28 November 1997 / Published online: 26 February 1998
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 Inöuï- 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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Online publication: August 4, 1998
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