Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-05-28
Helv.Phys.Acta 69 (1996) 141
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 16 pages, no figures, to be published in Helv. Phys. Acta
Scientific paper
The representation theory of deformed oscillator algebras, defined in terms of an arbitrary function of the number operator~$N$, is developed in terms of the eigenvalues of a Casimir operator~$C$. It is shown that according to the nature of the $N$ spectrum, their unitary irreducible representations may fall into one out of four classes, some of which contain bosonic, fermionic or parafermionic Fock-space representations as special cases. The general theory is illustrated by classifying the unitary irreducible representations of the Arik-Coon, Chaturvedi-Srinivasan, and Tamm-Dancoff oscillator algebras, which may be derived from the boson one by the recursive minimal-deformation procedure of Katriel and Quesne. The effects on non-Fock-space representations of the minimal deformation and of the quommutator-commutator transformation, considered in such a procedure, are studied in detail.
Quesne Christiane
Vansteenkiste N.
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