1994/05/20 by Shahn Majid, Henri Ruegg · 1 citation
Mathematics · Physics and Astronomy · #hep-th #math.QA
paper · pdf · doi:10.1016/0370-2693(94)90699-8
published as Phys.Lett. B334 (1994) 348-354 · 12 pages. Revision: minor typos corrected
arxiv created 1994/05/20 · arxiv updated 2009/11/30
We show that the κ-deformed Poincaré quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct U(so(1,3))\cobicross T. The algebra is a semidirect product of the classical Lorentz group so(1,3) acting in a deformed way on the momentum sector T. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the κ-Poincaré acts covariantly on a κ-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.