Two-parameter deformation of the Poincaré algebra

Abstract

We examine a two-parameter ($\hbar ,$ $λ$) deformation of the Poincarè algebra which is covariant under the action of $SL_q(2,C).$ When $λ\rightarrow 0$ it yields the Poincarè algebra, while in the $\hbar\rightarrow 0$ limit we recover the classical quadratic algebra discussed previously in \cite{ssy95}, \cite{sy95}. The analogues of the Pauli-Lubanski vector $w$ and Casimirs $p^2$ and $w^2$ are found and a set of mutually commuting operators is constructed.