(Heisenberg-)Weyl Algebras, Segal-Bargmann Transform and Representations of Poincaré Groups

Abstract

In a recent paper [1] we described a novel treatment of the unitary irreducible representations of the Poincaré groups in 2, 3 and 4 space-time dimensions as unitary operators on the representation spaces of the Schrödinger representation of the Heisenberg-Weyl algebra of index r = 1, 2, and 3, respectively. Here we relate this approach to the usual method of describing the representations of these Poincaré groups, i.e. the Wigner-Mackey construction.