On 3+1 anti-de Sitter and de Sitter Lie bialgebras with dimensionful deformation parameters

Details On 3+1 anti-de Sitter and de Sitter Lie bialgebras with dimensionful deformation parameters On 3+1 anti-de Sitter and de Sitter Lie bialgebras with dimensionful deformation parameters

2004-08-26

arxiv.org/abs/hep-th/0408196v2

Czech.J.Phys. 54 (2004) 1321-1327

Physics

High Energy Physics

High Energy Physics - Theory

7 pages. Communication presented in the XIII Int.Colloq. Integrable Systems and Quantum Groups, June 17-19, 2004, Prague, Czec

Scientific paper

We analyze among all possible quantum deformations of the 3+1 (anti)de Sitter algebras, so(3,2) and so(4,1), which have two specific non-deformed or primitive commuting operators: the time translation/energy generator and a rotation. We prove that under these conditions there are only two families of two-parametric (anti)de Sitter Lie bialgebras. All the deformation parameters appearing in the bialgebras are dimensionful ones and they may be related to the Planck length. Some properties conveyed by the corresponding quantum deformations (zero-curvature and non-relativistic limits, space isotropy,...) are studied and their dual (first-order) non-commutative spacetimes are also presented.

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