Positive-energy irreps of the quantum anti de sitter algebra

V. K. Dobrev, P. J. Moylan

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Abstract

We obtain positive-energy irreducible representations of the q-deformed anti de Si tter algebra Uq(so(3, 2)) by deformation of the classical ones. When the deformation parameter q is N-th root of unity, all these irreducible representations become unitary and finite-dimensional. Generically, their dimensions are smaller than those of the corresponding finite-dimensional non-unitary representations of so(3, 2). We discuss in detail the single-ton representations, i.e. the Di and Rac. When N is odd, the Di has dimension 1/2(N2 - 1) and the Rac has dimension 1/2(N2 + 1), while if N is even, both the Di and Rac have dimension 1/2N2. These dimensions are classical only for N = 3 when the Di and Rac are deformations of the two fundamental non-unitary representations of so(3, 2).

Original languageEnglish (US)
Pages (from-to)171-178
Number of pages8
JournalCzechoslovak Journal of Physics
Volume46
Issue number2-3
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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