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
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