Representations of the Bondi—Metzner—Sachs group I. Determination of the representations

Abstract
Following a historical introduction, it is suggested that irreducible unitary representations of the Bondi-Metzner-Sachs group may be used to classify elementary particles in a quantum theory which takes 'asymptotically flat' gravitational fields into account. The unitary representations of the group induced from irreducible unitary representations of the connected little groups are all determined. It is shown that the connected little groups are all compact, so that the 'spins' of the corresponding particles are necessarily discrete, and the wavefunctions have a finite number of components. Furthermore, the spins are of precisely the observed type. This is in striking contrast to the situation for the Poincare group, for which the spins may be discrete or continuous. (The continuous spin wavefunctions are infinite-component). It is concluded that the B.M.S. group may provide an explanation for the observed discreteness of the spins of elementary particles.

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