Eur. Phys. J. C (2006) 48: 633-639
https://doi.org/10.1140/epjc/s10052-006-0024-6

Theoretical Physics

Jordanian twist quantization of D=4 Lorentz and Poincaré algebras and D=3 contraction limit

¹ Institute for Theoretical Physics, University of Wrocław, pl. Maxa Borna 9, 50–205, Wrocław, Poland
² Institute of Nuclear Physics, Moscow State University, 119992, Moscow, Russia

^* e-mail: lukier@ift.uni.wroc.pl

Received: 24 April 2006
Published online: 24 October 2006

Abstract

We describe in detail the two-parameter nonstandard quantum deformation of the D=4 Lorentz algebra , linked with a Jordanian deformation of . Using the twist quantization technique we obtain the explicit formulae for the deformed co-products 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 a dimensionless deformation parameter. Finally, we interpret as the D=3 de Sitter algebra and calculate the contraction limit (R is the de Sitter radius) providing an explicit Hopf algebra structure for the quantum deformation of the D=3 Poincaré algebra (with mass-like deformation parameters), which is the two-parameter light-cone κ-deformation of the D=3 Poincaré symmetry.