How can particles undergo EM interactions *and* have definite strong isospin?by depeche1 Tags: commutation, electromagnetism, hadrons, isospin 

#1
Apr2111, 03:26 AM

P: 1

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 stateindependent properties that define a proton are strong isospin Iz=1/2 and charge Q=e. Now, the total Hamiltonian for a proton is
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 +Hwp> = mp> where p> is the wavefunction of the proton. Since Iz=1/2 and charge Q=e are two of the stateindependent properties that define the proton, presumably this means that Hs +Hem +HwIz=1/2, Q=e> = mIz=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! 



#2
Apr2111, 05:20 AM

Sci Advisor
Thanks
P: 3,856

The charge operator Q = I_{z} + Y/2, where Y is the hypercharge. For protons and neutrons, Y = 1. The electromagnetic Hamiltonian does not commute with I_{z} by itself, or Y by itself, but it does commute with the combination Q.
It also commutes with I. Protons and neutrons form an isospin doublet with I = 1/2. 



#3
Apr2111, 05:59 AM

P: 115




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