The strong isospin raising operator changes a d quark into a u: τ+|d⟩=|u⟩
However, for antiquarks, there is an additional phase factor: τ+|ˉu⟩=−|ˉd⟩
This phase factor is the reason the π0 wavefunction is proportional to |uˉu⟩−|dˉd⟩. But I don't understand why it arises.
The book that I have at hand is Wong's Nuclear Physics. Given particle creation operators a†t,t0 and antiparticle creation operators b†t,t0 for hadrons with strong isospin t and projection t0, Wong states that b†t,t0=(−1)t−t0at,−t0
because "operators a†t,t0 and at,−t0 are not Hermitian conjugate of each other without the factor (−1)t−t0." There is supposedly a more detailed argument in Bohr & Mottleson, which I don't have access to at the moment.
- Why is this phase factor required?
- Do the same symmetry arguments apply to weak isospin partners? If so, I need to revise my opinion on this previous question.
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