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 flat5 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 wave functions 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 wave functions 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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4. Cantoni V. 1967 a Ph.D . Thesis University of London. (The fact that the B.M.S. group has a semi-direct product structure was first recognized in this reference by Cantoni and also by Foster J. The particular representation of the Lorentz group on A which specifies this structure was noticed independently by the author and by Geroch R. J. & Newman E. T. Math. Phys. 12 no. 2314 (1971). A note on the structure of the group by the author will appear shortly.)
5. Cantoni V. 19676 Accad. N az. Line. (13) 43 30.
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