κ\kappa-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations

We consider $\kappa$-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincar\'e algebra is unaltered, while the other is a general extension where the Poincar\'e algebra is deformed. As an example we fix the Jordanian twist and the corresponding realization of noncommutative coordinates, coproduct of momenta and addition of momenta. An extension with a one-parameter family of realizations of the Lorentz generators, dilatation and momenta closing the Poincar\'e-Weyl algebra is considered. The corresponding physical interpretation depends on the way the Lorentz algebra is implemented in phase space. We show how the spectrum of the relativistic hydrogen atom depends on the realization of the generators of the Poincar\'e-Weyl algebra.Comment: Title changed and minor changes in the tex

Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime

We propose a generalized description for the kappa-Poincare-Hopf algebra as a symmetry quantum group of underlying kappa-Minkowski spacetime. We investigate all the possible implementations of (deformed) Lorentz algebras which are compatible with the given choice of kappa-Minkowski algebra realization. For the given realization of kappa-Minkowski spacetime there is a unique kappa-Poincare-Hopf algebra with undeformed Lorentz algebra. We have constructed a three-parameter family of deformed Lorentz generators with kappa-Poincare algebras which are related to kappa-Poincare-Hopf algebra with undeformed Lorentz algebra. Known bases of kappa-Poincare-Hopf algebra are obtained as special cases. Also deformation of igl(4) Hopf algebra compatible with the kappa-Minkowski spacetime is presented. Some physical applications are briefly discussed.Comment: 15 pages; journal version; Physics Letters B (2012

Kappa-deformation of phase space; generalized Poincare algebras and R-matrix

We deform Heisenberg algebra and corresponding coalgebra by twist. We present undeformed and deformed tensor identities. Coalgebras for the generalized Poincar\'{e} algebras have been constructed. The exact universal $R$-matrix for the deformed Heisenberg (co)algebra is found. We show, up to the third order in the deformation parameter, that in the case of $\kappa$-Poincar\'{e} Hopf algebra this $R$-matrix can be expressed in terms of Poincar\'{e} generators only. This implies that the states of any number of identical particles can be defined in a $\kappa$-covariant way.Comment: 10 pages, revtex4; discussion enlarged, references adde