Eur. Phys. J. C (2013) 73: 2472
https://doi.org/10.1140/epjc/s10052-013-2472-0

Regular Article - Theoretical Physics

Differential forms and κ-Minkowski spacetime from extended twist

¹ Rudjer Bošković Institute, Bijenička c.54, 10002, Zagreb, Croatia
² Jacobs University Bremen, 28759, Bremen, Germany

^* e-mail: tjuric@irb.hr

Received: 24 April 2013
Published online: 2 July 2013

Abstract

We analyze bicovariant differential calculus on κ-Minkowski spacetime. It is shown that corresponding Lorentz generators and noncommutative coordinates compatible with bicovariant calculus cannot be realized in terms of commutative coordinates and momenta. Furthermore, κ-Minkowski space and NC forms are constructed by twist related to a bicrossproduct basis. It is pointed out that the consistency condition is not satisfied. We present the construction of κ-deformed coordinates and forms (super-Heisenberg algebra) using extended twist. It is compatible with bicovariant differential calculus with κ-deformed -Hopf algebra. The extended twist leading to κ-Poincaré-Hopf algebra is also discussed.