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

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√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√q(2) algebra, contrary to current belief in the literature.