• Citer

Representation theory of generalized deformed oscillator algebras

par Quesne, Christiane ;Vansteenkiste, Nicolas
Référence Czechoslovak Journal of Physics, 47, 1, page (115-122)
Publication Publié, 1997-01

Article révisé par les pairs

• Détails
• Contenu

Résumé :

The representation theory of the generalized deformed oscillator algebras (GDOA's) is developed. GDOA's are generated by the four operators {1, a, a†, N}. Their commutators and Hermiticity properties are those of the boson oscillator algebra, except for [a, a†] q = G(N), where [a, b] q = ab - q ba and G(N) is a Hermitian, analytic function. The unitary irreductible representations are obtained by means of a Casimir operator C and the semi-positive operator a†a. They may belong to one out of four classes: bounded from below (BFB), bounded from above (BFA), finite-dimentional (FD), unbounded (UB). Some examples of these different types of unirreps are given.