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