- #1
HomogenousCow
- 737
- 213
I'm currently doing a course on the Standard Model and I think I've gotten confused on some of the symmetries and resulting currents. Here's my current understanding:
Before SSB:
Electroweak - U(1) symmetry on fermion spinors and Higgs complex doublet, 1 conserved current
Electroweak - SU(2) symmetry on Higgs complex doublet, quark and lepton spinor doublets (left-handed spinors), 3 conserved currents
Color - SU(3) symmetry on quark spinor triplets, 8 conserved currents
After SSB:
EM - U(1) residual symmetry on fermion spinors, 1 conserved current
Color - Same as before, 8 conserved currents
So my questions are follows:
1. Are the 3 currents from SU(2) completely gone after SSB?
2. Why must the Higgs field lose U(1) symmetry after SSB? It feels arbitrary that the Higgs field is chosen to be real after SSB.
3. Why do we talk about "color conservation" when there are in fact 8 conserved currents due to SU(3)?
4. I've read about a conserved "baryon number" due to U(1) symmetry, is this another distinct U(1) symmetry?
5. Why do the W-bosons carry electric charge?? Do they participate in the residual U(1) symmetry?
Before SSB:
Electroweak - U(1) symmetry on fermion spinors and Higgs complex doublet, 1 conserved current
Electroweak - SU(2) symmetry on Higgs complex doublet, quark and lepton spinor doublets (left-handed spinors), 3 conserved currents
Color - SU(3) symmetry on quark spinor triplets, 8 conserved currents
After SSB:
EM - U(1) residual symmetry on fermion spinors, 1 conserved current
Color - Same as before, 8 conserved currents
So my questions are follows:
1. Are the 3 currents from SU(2) completely gone after SSB?
2. Why must the Higgs field lose U(1) symmetry after SSB? It feels arbitrary that the Higgs field is chosen to be real after SSB.
3. Why do we talk about "color conservation" when there are in fact 8 conserved currents due to SU(3)?
4. I've read about a conserved "baryon number" due to U(1) symmetry, is this another distinct U(1) symmetry?
5. Why do the W-bosons carry electric charge?? Do they participate in the residual U(1) symmetry?
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