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

1997/10/10 by Harold Steinacker, Steinacker, Harold
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9710016

3 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

arxiv created 1997/10/10 · arxiv updated 2009/11/30

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 ≥ 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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