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I EM field strength tensor

  1. Jan 25, 2017 #1

    dyn

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    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. jcsd
  3. Jan 26, 2017 #2

    Orodruin

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    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.
     
  4. Jan 26, 2017 #3

    dyn

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    Thanks for your reply. It all works out now.
     
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