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Hey I'm trying to follow the derivation given here: http://lampx.tugraz.at/~hadley/ss1/studentpresentations/Bloch08.pdf
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?
Some tensor product rule maybe?
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
Homework Statement
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?
Homework Equations
Some tensor product rule maybe?
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