I am deeply confused about the following and I'd really appreciate it if anyone could help! Consider a charged hadron such as a proton. Amongst the state-independent properties that define a proton are strong isospin Iz=1/2 and charge Q=e. Now, the total Hamiltonian for a proton is(adsbygoogle = window.adsbygoogle || []).push({});

Hs +Hem +Hw,

where these denote the strong, electromagnetic and weak interaction Hamiltonians respectively. And in the rest frame of the proton p, which has mass m, we have

Hs +Hem +Hw|p> = m|p>

where |p> is the wavefunction of the proton. Since Iz=1/2 and charge Q=e are two of the state-independent properties that define the proton, presumably this means that

Hs +Hem +Hw|Iz=1/2, Q=e> = m|Iz=1/2, Q=e>

- otherwise it wouldn't be the eigenvalue equation for a proton wavefunction. But the electromagnetic Hamiltonian Hem does not commute with Iz; so how can the proton be evolving in accordance with the above Hamiltonian *and* have definite isospin?!

Any help really appreciated!

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# How can particles undergo EM interactions *and* have definite strong isospin?

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