POINCARE CONTRACTION OF SU(1,1) FOCK-BARGMANN STRUCTURE

Some aspects of the contraction process SO0(1, 2) to Poincare are stud ied in this paper. The starting point is the choice of a suitable para metrization for the de Sitterian phase space SO0(1, 2)/SO(2) congruent -to SU(1, 1)/U(1). We show that the contraction to Poincare must be re alized by restricting the Fock-Bargmann space to a specific subspace. This constraint is necessary to make the divergent terms disappear. In particular, the classical result according to which the discrete seri es representation of SU(1, 1) contracts onto the Wigner representation P(m) is described at a global level.