- #1
LAHLH
- 409
- 1
Hi
In ch84, Srednicki is considering the gauge group SU(N) with a real scalar field [itex]\Phi^a[/itex] in the adjoint rep. He then says it will prove more convienient to work with the matrix valued field [itex]\Phi=\Phi^a T^a [/itex] and says the covariant derivative of this is [itex] D_{\mu}\Phi=\partial_{\mu}\Phi-igA^a_{\mu}\left[T^a,\Phi\right][/itex]
Why is this covariant derivative not just [itex] D_{\mu}\Phi=\partial_{\mu}\Phi-igA^a_{\mu}T^a\Phi[/itex] ?
I understand [itex]\Phi [/itex] is a matrix and it does not commute with the generators, but I don't understand how this commutator is arising here in the second term of the covariant derivative? is it something to do with the adjoint rep?
In ch84, Srednicki is considering the gauge group SU(N) with a real scalar field [itex]\Phi^a[/itex] in the adjoint rep. He then says it will prove more convienient to work with the matrix valued field [itex]\Phi=\Phi^a T^a [/itex] and says the covariant derivative of this is [itex] D_{\mu}\Phi=\partial_{\mu}\Phi-igA^a_{\mu}\left[T^a,\Phi\right][/itex]
Why is this covariant derivative not just [itex] D_{\mu}\Phi=\partial_{\mu}\Phi-igA^a_{\mu}T^a\Phi[/itex] ?
I understand [itex]\Phi [/itex] is a matrix and it does not commute with the generators, but I don't understand how this commutator is arising here in the second term of the covariant derivative? is it something to do with the adjoint rep?