Positive energy representations of the conformal quantum algebra

Details Positive energy representations of the conformal quantum algebra Positive energy representations of the conformal quantum algebra

1993-03-19

arxiv.org/abs/hep-th/9303115v1

Phys.Lett. B302 (1993) 215-222

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, plain-TEX, preprint IC/92/187, SISSA 137/92/FM, UTS-DFT-22-92, (July 1992), Phys. Lett. 302B (1993) 215

Scientific paper

10.1016/0370-2693(93)90387-W

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 $h = \pm 1/2$.

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