All quarks, of course, have A = 1/3. The u and d quarks form an isospin doublet, T = 1/2, while the other four quarks are isospin singlets, T = 0. Quote from Wikipedia: “In modern descriptions of hadron interaction, it has become more obvious to draw Feynman diagrams that trace through individual quarks composing the interacting baryons and mesons, rather than counting hypercharge  (and other) quantum numbers.” The basic idea is that T commutes with strong interaction Hamiltonians, but not with electromagnetic Hamiltonians, which contain the charge Q which can be expressed in terms of T₃. Thus if you take a strongly interacting system and slowly turn on the electromagnetic force, it removes a degeneracy, breaking the initial single state into a multiplet, with each multiplet member having a different value of T₃ or Q.  In old multiplet diagrams, often strangeness S is used, as below.  In more modern or more general diagrams, hypercharge Y is used.

ISOSPIN IN NUCLEAR PHYSICS

In nuclear physics, the neutron is taken to have T₃ = +1/2 and the proton to have T₃ = -1/2.  [This is the exact opposite of the convention in particle physics.]

The isobaric analog state of a bound single-neutron state in heavier nuclei is found as an unbound state, an isobaric analog resonance, in the corresponding nucleus where the neutron is replaced by a proton in the same level.

Isospin decomposition is handled just the same way as angular momentum or spin decomposition, by use of Clebsch-Gordan coefficents.



As we said earlier, the Nobel Prize in Physics 1963, was awarded to Eugene Paul Wigner, for  "the discovery and application of fundamental symmetry principles.” Wigner was one of “the Martians.” Do you recognize his fellow Hungarian in this photo?  Yet, these symmetry ideas were very unpopular in the early 1960s.  In a YouTube interview with Murray Gell-Mann, he tells the story of how when he proposed giving a lecture on isospin at various universities, he was always told, "Nobody cares about any of that stuff, but we would be happy for you to lecture on some other topic." Things changed drastically by the mid-1960s... soon everyone wanted to hear about symmetries and group theory!

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