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

Abstract

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 $\ge 1$, 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.

arXiv comment3 pages, one figure using epsf, uses sprocl.sty available at http://www.wspc.demon.co.uk/Styles/procs/ . Submitted to Proc.WigSym5, Vienna, Austria, 25-29 August, 1997

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