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SU(2) isospin |
τx,τy, τz (τ+ τ- τz and τ2) |
Pairs u,d quarks (originally, neutron and proton) for the construction and properties of hadrons. |
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SU(3) favor |
U±, V±, T±, T3, Λ8 |
Combines u,d,s for building hadrons. Extension of SU(2) |
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SU(3) color |
U±, V±, T±, T3, Λ8 |
Generates QCD related to the color charges (R,G,B) |
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U(1) charge |
Q |
Overall phase transformation that requires charge confirmation. |
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U(1) Baryon # |
B |
Overall phase transformation that requires Baryon number confirmation. |
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U(1) Hypercharge |
Y |
U(1) that leads to Electroweak |
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Translation |
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Rotation |
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Boost |
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SU(2)L weak isospin |
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Parity |
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U(1) baryon number |
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Charge conjugation |
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Time reversal |
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Note, all of the tranformations are ultimately some type of phase transformation. This is due to the unitarity requirement for the transforamtions on quantum states. More than one symmetry is required in our complete system. Our representation should be compatible with the symmetries required.