Recent content by Nazaf

So it was just a matter of exchanging the indices q and l in either one of terms, right?

I understand. How about the following? \begin{align} & -\frac{1}{4\mu_0} \left( F^{kq} F^{nl}g_{ql} + F^{nq} F^{kl}g_{ql} \right) \\ & = -\frac{1}{4\mu_0} \left( F^{kq} F^{ns}g_{qs} + F^{ns} F^{kl}g_{sl} \right) \\ & = -\frac{1}{4\mu_0} \left( F^{kl} F^{ns}g_{ls} + F^{ns} F^{kl}g_{sl} \right)...

I see. Is the following correct? F^{kq} F^{n}_q + F^{nq} F^{k}_q = F^{kq} F^{n}_q + \delta^k_n \delta^n_k F^{nq} F^{k}_q \\ = F^{kq} F^{n}_q + F^{nq} F^{n}_q

Which terms are the same? Can you explain more?

I already tried. Here is what I got: \frac{\partial}{\partial g_{kn}} (g_{pj}g_{ql}) = \frac{\partial g_{pj}}{ \partial g_{kn}} g_{ql} + g_{pj} \frac{\partial g_{ql}}{\partial g_{kn}} Because the metric tensor is symmetric: g_{pj} = \frac{1}{2} (a_{pj} + a_{jp}) \frac{\partial}{\partial...

\mathcal{L}_M(g_{kn}) = -\frac{1}{4\mu{0}}g_{kj} g_{nl} F^{kn} F^{jl} \\ \frac{\partial{\mathcal{L}_M}}{\partial{g_{kn}}}=-\frac{1}{4\mu_0}F^{pq}F^{jl} \frac{\partial}{\partial{g_{kn}}}(g_{pj}g_{ql})=+\frac{1}{4\mu_0} F^{pq} F^{lj} 2 \delta^k_p \delta^n_j g_{ql} I need to know how...