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

TL;DR

This paper explores a deformation of the Heisenberg algebra and Poincaré algebra using twist methods, deriving an explicit R-matrix that enables a covariant description of multi-particle states in κ-Poincaré quantum groups.

Contribution

It constructs the deformed coalgebra structures for generalized Poincaré algebras and derives an explicit universal R-matrix for the κ-deformed Heisenberg algebra.

Findings

Universal R-matrix expressed in terms of Poincaré generators

Deformation preserves covariant multi-particle states

Explicit third-order deformation results obtained

Abstract

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.