Hi(adsbygoogle = window.adsbygoogle || []).push({});

In ch84, Srednicki is considering the guage 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Covariant deriv of matrix valued field(srednicki)

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**