Realization of the discrete series of unitary representations of Sl(2,R) in terms of creation and annihilation operators

Abstract

A basis for the Hilbert space of the discrete series of unitary representations of Sl(2,R) is constructed as a complete set of coherent states of pairs of particle–antiparticle creation operators. The integer q specifying an irreducible representation is the eigenvalue of the charge operator. Representations with charges ∓q are equivalent.