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 $s{u}_{\sqrt{q}}(2)$ 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 $s{u}_{\sqrt{q}}(2)$ algebra, contrary to current belief in the literature.

Needs Ljour2.sty and subeqnarray. Changes made to text with some references added. To appear in Z. Phys. 1998

References in corpus (5)

• Q-Deformed Oscillator Algebra and an Index Theorem for the Photon Phase Operator
• Representation Theory of Generalized Deformed Oscillator Algebras
• A Schwinger term in q-deformed su(2) algebra
• Quantum group covariant systems
• Real Forms of the Oscillator Quantum Algebra and its Representations

Cited by in corpus (1)

• Unified $(p,q;\alpha ,\gamma ,l)$-deformation of oscillator algebra and two-dimensional conformal field theory