Representations of the Bondi-Metzner—Sachs group III. Poincaré spin multiplicities and irreducibility

It has been conjectured that representations of the B.M.S. group may be of relevance to the classification of elementary particles. In an effort to examine this conjecture, the Poincaré spin multiplicities occurring in each induced B.M.S. representation are calculated. For positive mass squared, direct sums of discrete Poincaré spins occur. For non-positive mass-squared, direct integrals of continuous Poincaré spins (together with, possibly, direct sums as well for negative mass squared) occur, though the Bondi spins are always discrete. It is proved that all induced B.M.S. representations (and hence also those of Komar’s factor group I) are irreducible.