Hi, I originally posted this in the maths forum but perhaps I should have posted in Physics to begin with, basically,
I have a Lagrangian:
Unparseable latex formula:\mathcal{L}=\dfrac {-1} {16\pi }\left( \partial ^{\mu }A^{\nu}\right -\partial ^{\nu }A^{\mu })\left( \partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }\right)+\dfrac {1} {8\pi }\left( \dfrac {mc} {h}\right) ^{2}A^{\nu }A_{\nu }
and I need to get to the result:
∂(∂μAv)∂L=−4π1(∂μAν−∂νAμ)The answer in the book that I'm working through does this by first finding the answer for all components involving
∂0A1 and its contraction. I can follow this method fine and it gives the correct result for that choice of indices and then it just generalises it.
However, I'd much rather know how to do using the general indices the entire way through, as I need to know this kinda stuff for my general relativity course.
I've managed to get to:
(∂μAν−∂νAμ)(∂μAν−∂νAμ)=−(∂μAν)2−∂μAν∂νAμ−∂νAμ∂μAν−(∂νAμ)2Could someone show me what to do next? I haven't got a clue, I'm not very good at being able to manipulate the indices.
Thaanks! I'll give rep to whoever helps if that's any incentive