I am studying the Faddeev-Popov method from Pokorski's Gauge Theory book, and I am puzzled by what happens in the step below.
He is writing the group element $g = 1 - i T_a\ \Theta^a(x)$ in a neighborhood of the identity, and then using... the chain rule? At least I though so, but then I can't understand why there is no $i$ factor in equation $(3.11)$.
Is he not using the chain rule? Where does that factor go?
For context: $g$ is an element of the Gauge group, $F^a$ are $n$ functionals (where $n$ is the dimention of the local gauge group), $A_\mu$ is the connection form and and $A_\mu ^g$ is the transformed $A_\mu$ under the action of $g$.