For [tex] -\frac{1} {4} F_{\mu\nu} F^{\mu\nu} [/tex] We can write [tex] -\frac{1} {4} F_{i j} F^{ij} -\frac{1}{2}F_{0i} F^{0i} [/tex] Where [tex] F_{\mu\nu} \equiv \partial_\mu W_\nu-\partial_\nu W\mu [/tex](adsbygoogle = window.adsbygoogle || []).push({});

If there are 3 indices how can I separate them like this?

I want to separate [tex] \frac{1} {12} G_{\mu\nu\rho} G^{\mu\nu\rho} [/tex] into time and space component . Where [tex] G_{\mu\nu\rho}\equiv\partial_{\mu}\phi_{\nu\rho}+ \partial_{\nu}\phi_{\rho\mu}+\partial_{\rho}\phi_{\mu\nu} [/tex]

How can I do it?

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# Divide in space and time component

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