Bicrossproduct structure of $κ$-Poincare group and non-commutative geometry

Details Bicrossproduct structure of $κ$-Poincare group and non-commutative geometry Bicrossproduct structure of $κ$-Poincare group and non-commutative geometry

1994-05-17

arxiv.org/abs/hep-th/9405107v2

Phys.Lett. B334 (1994) 348-354

Physics

High Energy Physics

High Energy Physics - Theory

12 pages. Revision: minor typos corrected

Scientific paper

10.1016/0370-2693(94)90699-8

We show that the $\kappa$-deformed Poincar\'e 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 $\kappa$-Poincar\'e acts covariantly on a $\kappa$-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.

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