Isospin

The two nucleon types 'Proton' and 'Neutron' just differ by their charge +1, 0, and by a rather tiny mass difference, less than 0.05 percent. Thus it was an attractive concept to see them as two different quantum states of the same particle, with their different charge, and slightly different energy. Just as the spin 'up' or 'down' describe two different states of the same particle, the property list of the nucleon is now enlarged by theisospin, and its '3-component'. The Algebra could well be the same as the spin, with just two states to describe. This has been gloriously tested in experiment.

$$\vert 1/2, \, \pm 1/2; \, 1/2, \, \pm 1/2; \, m, \, q, \, \psi\!>$$ (10)

with the complete list of properties for an electron: (spin, spincomponent in 3-direction, isopin, isopincomponent in 3-direction, mass, chage, probability-amplitude). Of course the '3-direction' of spin and isopspin are in their own spaces, not in spatial space.