Consider the $SU(3)$ part of the standard model. It appears that every fundamental particle in the standard model either lives in the trivial (leptons), the fundamental representation (quarks), or the antifundamental representation (antiquarks). Generalizing this idea, it appears that matter in the standard model does not live in higher irreducible representations of the gauge group $G$. Is there some a priori reason why this must be true? Moreover, if it isn't exactly true that this is satisfied in the standard model, correct me where I am wrong.

  • $\begingroup$ There are the baryon resonances that occupy higher representations of weakk SU(3) . en.wikipedia.org/wiki/Eightfold_Way_(physics). Quarks and leptons do not have excited states . $\endgroup$ – anna v Nov 6 '17 at 7:54
  • $\begingroup$ You also have gluons in the adjoint representation. $\endgroup$ – Antoine Nov 6 '17 at 8:39
  • $\begingroup$ That is why I said fundamental (not composite) particles, and matter (bit gauge bosons). Also the weak $SU(3)$ symmetry isn't a gauge symmetry. $\endgroup$ – Bob Knighton Nov 6 '17 at 14:01
  • $\begingroup$ Yes so far, fundamental fermions are in the fundamental reps. A "just so" statement of natural fact. Could change in future. $\endgroup$ – Cosmas Zachos Apr 9 at 0:23

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