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I'm studying electroweak spontaneous symmetry breaking at that time, see for instance Chang and Li's book ch 11. Have any one an idea that if the charge operator is defined by:

## Q = \int (- e^\dagger e + \frac{2}{3} u^\dagger u - \frac{1}{3} d^\dagger d ) d^3 x ,##

and the isospin operator defined by :

## T_3 = \frac{1}{2} \int (\nu^\dagger_L \nu_L - e^\dagger_L e_L + u^\dagger_L u_L - d^\dagger_L d_L ) d^3 x, ##

why when the electric charge operator acting on the vacuum expectation value ##\phi_0 = <0|\phi|0> = (0~~~~~~ v)^T ## it gives zero, i.e., ## Q <\phi>_0 = 0 ## , while when the isospin operator or the hypercharge = ##Q-T_3## acting on the VEV it doesn't vanish ?

So that we say the electric charge still conserved after EWSSB while the hypercharge or isospin has been broken

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# I Unbroken electromagnetic symmetry

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