Construction of Simple $q$-Deformed Algebras by Statistics

Details Construction of Simple $q$-Deformed Algebras by Statistics Construction of Simple $q$-Deformed Algebras by Statistics

1994-02-16

arxiv.org/abs/hep-th/9402090v1

Physics

High Energy Physics

High Energy Physics - Theory

15pages, JUTP-94-1, hep-th/yymmnnn, LaTeX

Scientific paper

The simple algebras of a dressed operator, which is composed of a dressing and a residual operators, are averaged following a proper statistics of the dressing one. In the Bose-Einstein statistics, a (fermionic) Calogero-Vasiliev oscillator, $q$-boson (fermion), and (fermionic) $su_q(1,1)$ are obtained for each bosonic (fermionic) residual operator. In the Fermi-Dirac statistics, new similar algebras are derived for each residual operator. Constructions of dual $q$-algebras, such as a dual Calogero-Vasiliev oscillator, a dual $q$-boson and a $su_q(2)$, and prospects are discussed.

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