Unitary Representations and BRST Structure of the Quantum Anti--de Sitter Group at Roots of Unity

Details Unitary Representations and BRST Structure of the Quantum Anti--de Sitter Group at Roots of Unity Unitary Representations and BRST Structure of the Quantum Anti--de Sitter Group at Roots of Unity

1997-10-10

arxiv.org/abs/q-alg/9710016v1

Physics

High Energy Physics

High Energy Physics - Theory

3 pages, one figure using epsf, uses sprocl.sty available at http://www.wspc.demon.co.uk/Styles/procs/ . Submitted to Proc.Wig

Scientific paper

It is shown that for suitable roots of unity, there exist finite--dimensional unitary representations of $U_q(so(2,3))$ corresponding to all classical one-particle representations with (half)integer spin, with the correct low-energy limit. In the massless case for spin $\geq 1$, a subspace of "pure gauges'' appears which must be factored out, as classically. Unitary many-particle representations are defined, with the same low-energy states as classically. Furthermore, a remarkable element of the center of $U_q(so(2,3))$ is identified which plays the role of the BRST operator, for any spin. The corresponding ghosts are an intrinsic part of indecomposable representations.

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