Irreducibility of the Ladder Representations of U(2, 2) when Restricted to the Poincaré Subgroup

Abstract

It is shown that the most degenerate discrete series of unitary irreducible representations of U(2, 2), the so-called ladder representations, remain irreducible when restricted to representations of the Poincaré subgroup ISL(2, C). They correspond to representations of this subgroup with mass zero and arbitrary integer or half-integer helicity λ. The basis vectors of the canonical basis are calculated as functions of a lightlike 4-vector, which is formed by the simultaneous eigenvalues of the generators of the subgroup of translations.