Hi, I'm wondering how to prove the following...can you help me?(adsbygoogle = window.adsbygoogle || []).push({});

[itex]

F^{\mu \rho} G_{\rho \nu} = \eta^\mu_{\phantom{\mu}\nu} \mathbf{E} \cdot \mathbf{B}

[/itex]

[itex]

F^{\mu \nu} F_{\mu \nu} = -2\left(\mathbf{E}^2-\mathbf{B}^2\right)

[/itex]

[itex]

G^{\mu \nu} F_{\mu \nu} = -4\,\mathbf{E} \cdot \mathbf{B}

[/itex]

[itex]

G^{\mu \nu} G_{\mu \nu} = F^{\mu \nu} F_{\mu \nu}

[/itex]

[itex]F[/itex] is the electromagnetic tensor, [itex]G[/itex] is it's dual, [itex]\eta[/itex] is the metric tensor, [itex]\mathbf{E}[/itex] and [itex]\mathbf{B}[/itex] the electric and magnetic field respectively.

Thank you for your patience!

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# How would you prove that?

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