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Lagrangian Field Theory - Maxwell's Equations
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[QUOTE="king vitamin, post: 6029038, member: 134222"] If you're having trouble, it might be helpful if you do not use the indices [itex]\mu, v[/itex] in your Lagrangian so that you don't get confused with the indices in the derivative that you're taking. So for your case: [tex] L = -\frac{1}{2} \eta^{a c} \eta^{b d}(\partial_{a} A_b) (\partial_{c} A_d) + \frac{1}{2} \eta^{a b} \eta^{c d}(\partial_{a} A_b) (\partial_{c} A_d) [/tex] or [tex] L = \frac{1}{2}\left(\eta^{a b} \eta^{c d} - \eta^{a c} \eta^{b d}\right) (\partial_{a} A_b) (\partial_{c} A_d) [/tex] Then use the relation [tex] \frac{\partial }{\partial (\partial_\mu A_v)} (\partial_{a} A_b) = \delta^{\mu}_a \delta^{v}_b [/tex] repeatedly. Now that you're not reusing indices in different parts of your equations it may eliminate some confusion. [/QUOTE]
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Lagrangian Field Theory - Maxwell's Equations
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