ABSTRACT
Gell-Mann was trying to get a symmetry-breaking effect from the kaon couplings, in order to generate mass differences among the four baryon multiplets. This is an aspect that is present in the search for higher symmetries: perhaps they can explain the mass spectrum in terms of some kind of breakdown effect. Contributing much to the progress that has lately been made along these lines are the group-theoretical considerations developed by Gell-Mann and Okubo. Couplings and branching ratios, a mass spectrum, predictions of missing particles and quantum-number assignments, vector mesons, and a connection with the weak and electromagnetic interactions—every consideration of a symmetry has sought information on all five of these problems. The mathematical formulation of higher-symmetry schemes was provided by the theory of Lie groups, the main tools having been developed by Cartan and Weyl.
