Representations of the Bondi-Metzner-Sachs group

Some time ago Cantoni (J. Math. Phys.; 7: 1361; (1966)) constructed a class of representations of the Bondi-Metzner-Sachs group from representations of the Poincare group with positive mass squared. His method is here shown to be equivalent to an inducing procedure based on a little group of supermomentum space. The corresponding classes of representations arising from zero and negative mass squared are also found. In each case the little group is GAMMA (which double covers S0(2)), and the inducing procedure begins with a reducible representation of GAMMA, which explains why the procedure gives reducible representations. The decomposition into irreducibles is given in all cases, each irreducible being identified with a Bondi-Metzner-Sachs irreducible in the nuclear topology. (author)