Abstract
In the first of a series of papers on the global representation theory of SU(2, 2), with particular emphasis on the Poincaré subgroup, we study the two principal continuous series of unitary irreducible representations. These are defined by operators on Hilbert spaces of functions over a six-dimensional manifold, and after an automorphism of the group by a real orthogonal transformation [in precise analogy to that used in the mapping SU(1, 1) → SL(2, R)] we display these in such a form that the Poincaré subgroup SL(2, C) × T4 appears in a simple fashion. The generators of translations, dilations, Lorentz and special conformal transformations are given as differential operators, and by using these we find explicit expressions for the eigenvalues of the three Casimir operators of the group. Finally, we perform the reduction of the two series when restricted to the Poincaré group. It is found that all those principal series representations of P enter which allow a certain value of helicity.
Published Version
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