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I have a question about the notation used in Electrodynamics, for the Eq.6.5.10. Can anyone tell me why is the sign of the covariant derivative swapped when it's transformed to a contravariant derivative? But it doesn't change for index zero. Many Thanks .

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Charo
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el psy Congroo
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1 Answers1

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I think that the simplest explanation is the one given in the picture above. Starting from Maxwell's equation in vector form you realise that you can treat them as coming from a more general object (cf. this question). As for the derivatives, observe that $\partial^\mu = g^{\mu\nu}\partial_\nu = (\partial_0, -\partial_1,-\partial_2-\partial_3)$.

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Phoenix87
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