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Question about the derivation of the energy momentum tensor

  1. Nov 23, 2015 #1
    Hey I'm trying to follow the derivation given here: http://lampx.tugraz.at/~hadley/ss1/studentpresentations/Bloch08.pdf
    1. The problem statement, all variables and given/known data
    As it says in the pdf: "Based on Noether's theorem construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. [itex]L=-1/4 F^{μν} F_{μν}[/itex] where [itex]F_{μν}=∂_μA_ν-∂_νA_μ [/itex]
    I'm stuck at equation (11): [itex] \frac{δL}{δ(∂_μA_λ)}=-F^{μν} [/itex].
    Could someone help me understand how they get this result?

    2. Relevant equations
    Some tensor product rule maybe?

    3. The attempt at a solution
    I would get the result if I use the usual product rule. But how do I treat the indices?
    Any tips or redirects to where I can read about it is very appreciated :)

    Kind regards
    Alex
     
  2. jcsd
  3. Nov 26, 2015 #2

    MarcusAgrippa

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    Gold Member

    Write the Lagrangian density in terms of the derivatives of the vector potential.
    Then use the fact that
    ## \frac{\partial (\partial_\mu A_\nu)}{\partial (\partial_\sigma A_\tau)} = \delta^\mu_\sigma \delta^\nu_\tau ##
     
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