On the projective representations of the Bondi-Metzner-Sachs group

With the Bondi-Metzner-Sachs (BMS) group in general relativity as the main motivation and example, a theorem is proved which may be described as follo ws. Let G be a complex semisimple, connected and simply connected Lie group with compact real form K, and let A be a metrizable, complete and locally convex real topological vee tor space on which there is a continuous G acti on. Consider the semidirect product topological group G x(s) A (which is, i n general, infinite-dimensional) constructed naturally out of G and A. If t he set of equivalence classes of irreducible representations of K in A sati sfies certain hypotheses, then the second cohomology group of G x(s) A in t he sense of continuous group cohomology is trivial. When G = SL(2, C) and A is an appropriate function space of real-valued functions of the 2-sphere endowed with a specific. G action (e.g. A may consist of C-k, k greater tha n or equal to 3, real-valued functions defined on the 2-sphere), the semidi rect product group is title universal cover of the EMS group. The theorem i mplies the existence of lifting of the projective unitary representations o f the EMS group to the linear unitary representations of its universal cove r. In the quantum context when we consider massless quantum fields at null infinity of a non-stationary, asymptotically Minkowskian space-time, in pla ce of the projective unitary representations of the EMS group, there is no loss of generality in considering the linear unitary representations of its universal cover instead.