Representations of the Bondi-Metzner-Sachs group - II. Properties and classification of the representations

Abstract

A proof is given that all (and not merely all connected ) little groups of the B. M. S. group are compact, so that B. M. S. spins are discrete whether or not the little groups are connected. The representations not already known (those with non-connected little groups) are all determined. It is shown that the unfaithful representations give rise to all induced representations of the factor group I introduced by Komar. Sach’s conjecture that the ‘mass squared’ is represented by a constant in B. M. S. representations is verified. Restriction of the representations to the Poincaré subgroup shows that Sach’s conjecture that the representations contain a mixture of Poincaré spins is also true in general (though, of course, the representations have a unique ‘Bondi spin’). It is suggested that the new quantum numbers arising from representations of the non-connected little groups may, perhaps, be associated with ‘internal’ symmetries of elementary particles.