# I EM field strength tensor

1. Jan 25, 2017

### dyn

Hi
I am trying to follow the derivation in some notes I have for the field strength tensor using covariant derivatives defined by Du = ∂u - iqAu . The field strength is the defined by [ Du , Dv ] = -iqFuv
The given answer is Fuv = ∂uAv - ∂vAu .When I expand the commutator I get this answer but I have 2 terms left over which I presume should cancel but I don't understand why . I have the extra terms iq(Avu - Auv ) . Do these terms cancel and if so , why ?
Thanks

2. Jan 26, 2017

### Orodruin

Staff Emeritus
You are forgetting that this commutator is an operator that should act on something and it should be seen as the operator commutator. The $\partial A$ terms represent first multiplying by A then differentiating. Therefore $\partial A f = (\partial A) f + A \partial f$. Add the corresponding indices.

3. Jan 26, 2017