There are two standard stories floating around in modern particle physics:
- Spontaneous symmetry breaking can only happen in a QFT, like in the electroweak theory, because no tunneling between the degenerate vacuum states of the scalar field are possible. Otherwise we the ground state would be a superposition of the degenerate ground states. The reason for the non-tunneling is that we assume that the spatial volume is infinite an thus the tunneling amplitude is zero.
- When we investigate the vacuum of QCD, we observe that there are infinitely many degenerate vacua. However here the correct vacuum state is a superposition of all these possible degenerate vacua.
How does 2.) fit together with 1.)? Why is tunneling suddenly allowed in QCD while otherwise it is stated strongly that there is no tunneling between degenerate ground states in a QFT?
(My guess would be that the tunneling in QCD is localized (= hence the name instantons) and thus the tunneling amplitude is non-zero. However, I can't see why the same argument wouldn't hold in the electroweak theory. Shouldn't it be equally possible that there is localized tunneling? Is the reason that we haven't found any electroweak instanton solutions that could describe such tunneling?)