Representation theory of generalized deformed oscillator algebras

Authors: Quesne C.¹; Vansteenkiste N.²

Source: Czechoslovak Journal of Physics, Volume 47, Number 1, January 1997 , pp. 115-122(8)

Publisher: Springer

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Abstract:

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.

Language: English

Document Type: Research article

Affiliations: 1: Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium. Directeur de recherches FNRS; equesne@ulb.ac.be 2: Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium. nvsteen@ulb.ac.be

Publication date: 1997-01-01