Abstract
A classification of the representations to which self-conjugate multiplets may belong, is given both in the case of local and nonlocal symmetries. For local symmetries, when the mass of the particles in the multiplet is not zero, and/or when the spin is zero, Carruthers’ result is derived. Counterexamples to Carruthers’ theorem are given for nonlocal symmetries and for the zero-mass, nonzero-spin local case. Then it is shown that a certain class of nonlocal symmetries (including those for which Carruthers’ theorem is violated) can only occur in a theory with noninteracting fields (generalized free fields).
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