Three-dimensional quadratic algebras: some realizations and representations

Authors
Kumar, VS Bambah, BA Jagannathan, R
Citation
Vs. Kumar et al., Three-dimensional quadratic algebras: some realizations and representations, J PHYS A, 34(41), 2001, pp. 8583-8596
Citations number
39
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
34
Issue
41
Year of publication
2001
Pages
8583 - 8596
Database
ISI
SICI code
0305-4470(20011019)34:41<8583:TQASRA>2.0.ZU;2-4
Abstract
Four classes of three-dimensional quadratic algebra of the type [Q(0), Q(+/ -)] = +/-Q(+/-), [Q(+), Q(-)] = aQ(0)(2) + bQ(0) + c, where (a, b, c) are c onstants or central elements of the algebra, are constructed using a genera lization of the well known two-mode bosonic realizations of su(2) and su(1, 1). The resulting matrix representations and single variable differential operator realizations are obtained. Some remarks on the mathematical and ph ysical relevance of such algebras are given.