The Bondi—Metzner—Sachs group in the nuclear topology

Abstract

The Bondi-Metzner-Sachs group is topologized as a nuclear Lie group, and it is shown th at irreducible representations arise from either (i) transitive SL{2,C) actions on supermomentum space, or (ii) cylinder measures in supermomentum space with respect to which the SL(2,C) action is strictly ergodic. The irreducibles arising from transitive actions are shown to be induced, and most of the theorems from a previous analysis (in which the group was given a Hilbert topology) are generalized so as to apply here. All non-discrete closed subgroups of 2, C) are found, and this analysis is used to construct all induced representations whose little groups are not both discrete and infinite. In the previous analysis, there were exactly two connected little groups, SU{2) and r (T double covers $0(2)). In the present analysis, exactly one additional connected little group A (which double covers E{2)) arises for faithful representations (that is, those for which the mass squared is defined); the associated mass squared value is zero. Exactly one further connected little group arises;