Abstract
The discrete series of the conformal groupSU(2, 2) is realized on a Hilbert space of holomorphic functions over a bounded domain or the field theoretic tube domain. The boundary values of these functions form Hilbert spaces of distributions. For the realization over the tube domain the boundary distributions transform like classical spinorial fields with a continuous mass spectrum extending from zero to infinity. The reduction of these field realizations of the whole discrete series into unitary irreducible representations of the inhomogeneous Lorentz group is explicitly given.
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Rühl, W. Field representations of the conformal group with continuous mass spectrum. Commun.Math. Phys. 30, 287–302 (1973). https://doi.org/10.1007/BF01645506
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DOI: https://doi.org/10.1007/BF01645506