- #1
Safinaz
- 260
- 8
Hi all,
I'm studying electroweak spontaneous symmetry breaking at that time, see for instance Chang and Li's book ch 11. Have anyone 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
I'm studying electroweak spontaneous symmetry breaking at that time, see for instance Chang and Li's book ch 11. Have anyone 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