Classification of Particle Multiplets

Abstract

In the present paper we observe that in considering how particle states transform under $\Theta =CPT$ one cannot neglect internal symmetries, since $\Theta$ changes the signs of all conserved internal additive quantum numbers; and that, furthermore, if a physical theory admits a parity symmetry $\mathcal{P}$, this symmetry may also, like $\Theta$, effect an automorphism on the group of internal symmetries, as does, for example, $\mathrm{CP}$, the correct parity operator in the presence of weak interactions. We find all types of particle multiplets for massive particles that are compatible with local field theory, particle multiplets being defined as the irreducible corepresentations of the group obtained by extending the internal symmetry group by $\mathcal{P}$ and $\Theta$. Of the thirteen types that exist, only three occur in the various approximation schemes that are at present used to describe nature. The reason for the nonappearance of the other types is not to be found in the usual postulates of local field theory, because Lagrangian field-theoretical examples of all thirteen types do exist and are given.