A generalization of the Jordan – Schwinger map : classical version and its q – deformation
نویسندگان
چکیده
A generalization of the Jordan–Schwinger map: classical version and its q–deformation. Abstract 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 SL q (2, IR), E q (2) and H q (1). The U q (n) algebra is discussed in the same context.
منابع مشابه
On strongly Jordan zero-product preserving maps
In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...
متن کاملJordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the GellMann and Ne’eman SU(3) symmetry group matrices. We show that the elements of the Jordan-Schwinger map are the constant...
متن کاملOn graded classical prime and graded prime submodules
Let $G$ be a group with identity $e.$ Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce several results concerning graded classical prime submodules. For example, we give a characterization of graded classical prime submodules. Also, the relations between graded classical prime and graded prime submodules of $M$ are studied.
متن کاملThe second dual of strongly zero-product preserving maps
The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are dened. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of...
متن کاملA Schwinger term in q - deformed su ( 2 ) algebra ∗
An extra term generally appears in the q-deformed su(2) algebra for the deformation parameter q = exp 2πiθ, if one combines the Biedenharn-Macfarlane construction of q-deformed su(2), which is a generalization of Schwinger’s construction of conventional su(2), with the representation of the q-deformed oscillator algebra which is manifestly free of negative norm. This extra term introduced by th...
متن کامل