A generalization of the Jordan-Schwinger map: classical version and its q--deformation

Details A generalization of the Jordan-Schwinger map: classical version and its q--deformation A generalization of the Jordan-Schwinger map: classical version and its q--deformation

1993-10-08

arxiv.org/abs/hep-th/9310053v1

Int. J. Mod. Phys. A9 (1994) 5541

Physics

High Energy Physics

High Energy Physics - Theory

LATEX,21 pages,INFN-NA-IV-93/38,DSF-T-93/38

Scientific paper

For all three--dimensional Lie algebras the construction of generators in terms of functions on 4-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical Jordan--Schwinger map which is also given for the deformed algebras ${\cal {SL}}_{q}(2,\R)$, ${\cal E}_{q} (2)$ and ${\cal H}_q(1)$. The ${\cal U}_{q}(n)$ algebra is discussed in the same context.

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