%0 Journal Article
%T Positive energy representations of the conformal quantum algebra
%A L. Dabrowski
%A V. K. Dobrev
%A R. Floreanini
%A V. Husain
%J Physics
%D 1993
%I arXiv
%R 10.1016/0370-2693(93)90387-W
%X The positive-energy unitary irreducible representations of the $q$-deformed conformal algebra ${\cal C}_q = {\cal U}_q(su(2,2))$ are obtained by appropriate deformation of the classical ones. When the deformation parameter $q$ is $N$-th root of unity, all these unitary representations become finite-dimensional. For this case we discuss in some detail the massless representations, which are also irreducible representations of the $q$-deformed Poincar\'e subalgebra of ${\cal C}_q$. Generically, their dimensions are smaller than the corresponding finite-dimensional non-unitary representation of $su(2,2)$, except when $N=2$, $h=0$ and $N = 2 \vert h\vert +1$, where $h$ is the helicity of the representations. The latter cases include the fundamental representations with $h = \pm 1/2$.
%U http://arxiv.org/abs/hep-th/9303115v1