SU(6) and the Quark Model
DOI link for SU(6) and the Quark Model
SU(6) and the Quark Model book
In the spectrum of low-lying baryons, the octet with spin 1/2 and the decuplet with spin 3/2 are not very far apart in mass. Typical splittings between the octet and decuplet states are not so different from splittings within the SU(3) representations. Noticing this, in the 60’s, many physicists played with the idea of embedding SU(3) in some larger symmetry group that would connect the two representations. Because the baryons in the 8 and 10 have different spins, the larger group cannot commute with angular momentum. You might expect this to cause problems, because it means mixing up internal symmetries and spacetime symmetries, and indeed it does. But the problems do not show up until you try to make the theory relativistic. We will discuss some of this, and possible resolutions, later.