Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit

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dc.creatorBorowiec, A.
dc.creatorLukierski, J.
dc.creatorTolstoy, V. N.
dc.date2006-04-20
dc.date.accessioned2026-07-07T11:27:27Z
dc.date.available2026-07-07T11:27:27Z
dc.descriptionWe describe in detail two-parameter nonstandard quantum deformation of D=4 Lorentz algebra $\mathfrak{o}(3,1)$, linked with Jordanian deformation of $\mathfrak{sl} (2;\mathbb{C})$. Using twist quantization technique we obtain the explicit formulae for the deformed coproducts and antipodes. Further extending the considered deformation to the D=4 Poincaré algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with dimensionless deformation parameter. Finally, we interpret $\mathfrak{o}(3,1)$ as the D=3 de-Sitter algebra and calculate the contraction limit $R\to\infty$ ($R$ -- de-Sitter radius) providing explicit Hopf algebra structure for the quantum deformation of the D=3 Poincaré algebra (with masslike deformation parameters), which is the two-parameter light-cone $κ$-deformation of the D=3 Poincaré symmetry.
dc.description13 pages, no figures
dc.identifierhttps://arxiv.org/abs/hep-th/0604146
dc.identifierhttp://arxiv.org/abs/hep-th/0604146
dc.identifierEur.Phys.J.C48:633-639,2006
dc.identifierdoi:10.1140/epjc/s10052-006-0024-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/196151
dc.subjectHigh Energy Physics - Theory
dc.titleJordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit
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