Particle Charge Symmetries as R8 Subgroups

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Abstract
It is shown how the formalism of 8 × 8 Dirac matrices can be extended to include all the groups so far proposed as relevant to elementary‐particle charge symmetries: R4, R7, G2, SU3. These are all treated as subgroups of R8, which appears to determine the eightfold structure of the particle families, even before the particle interactions are ``switched on''. Since these subgroups of R8 are incompatible, they will lead to a ``clash of symmetries'', as observed experimentally. It is pointed out that if the plausible association is made between real and charge‐space statistics in representations of R8, the group SU3 satisfies charge‐conjugation invariance for 3‐boson interactions but not for two‐fermion‐one‐boson interactions. An argument is given that the representations 8 and 8̄ of SU3 plus the representations (7 + 1) of G2 and R7 completely span the symmetries obeying the limited invariance implied by conservation of isotopic spin I and hypercharge Y.

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