Abstract
Some aspects of the contraction process SO0(1,2) to Poincare are studied. The starting point is the choice of a suitable parametrization for the de Sitterian phase space SO0(1,2)/SO(2) approximately=SU(1,1)/U(1). The authors show that the contraction to Poincare must be realized 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 series representation of SU(1,1) contracts onto the Wigner representation P(m) is described at a global level.
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