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ψ → exp(iαaIa)ψ . |
[Ia,Ib]=iCcabIc . |
The Yang-Mills Lagrangian
L=i Dμ=∂μ-igBμ , Bμ≡ BaμIa |
Baμ → Baμ+1/gDμαa |
The generalization of the electro-magnetic tensor Fμν is the invariant tensor Gμν
Gμν = i[Dμ,Dν] = ∂μBν - ∂νBμ - ig[BμBν], |
LB = -1/4GaμνGaμν = -1/2TrGμνGμν |