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## Main Question or Discussion Point

Hi as I'm reading http://www.maths.tcd.ie/~cblair/notes/432.pdf at page 13 I see that he states that the covariant and contravariant field tensors are different. But how can that be? Aren't they related by

[tex] F_{\mu \nu} = \eta_{\nu \nu'} \eta_{\mu \mu '} F^{\mu ' \nu '} ?[/tex]

and is not the product of the metric tensor eta with it self the identity? I view this as a matrix product

[tex] F = \eta \eta F'[/tex]

and writing out either η or the metric g it seems like their product with eachother are the identity such that

[tex] F=\eta \eta F' = I F'.[/tex]

Where is my reasoning wrong?

At page 14 he derived two of the maxwell equations from a lagrangian. But what about the other two? The author just states them. Are not these derivable from a lagrangian?

[tex] F_{\mu \nu} = \eta_{\nu \nu'} \eta_{\mu \mu '} F^{\mu ' \nu '} ?[/tex]

and is not the product of the metric tensor eta with it self the identity? I view this as a matrix product

[tex] F = \eta \eta F'[/tex]

and writing out either η or the metric g it seems like their product with eachother are the identity such that

[tex] F=\eta \eta F' = I F'.[/tex]

Where is my reasoning wrong?

At page 14 he derived two of the maxwell equations from a lagrangian. But what about the other two? The author just states them. Are not these derivable from a lagrangian?