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aries0152
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For -\frac{1} {4} F_{\mu\nu} F^{\mu\nu} We can write -\frac{1} {4} F_{i j} F^{ij} -\frac{1}{2}F_{0i} F^{0i} Where F_{\mu\nu} \equiv \partial_\mu W_\nu-\partial_\nu W\mu
If there are 3 indices how can I separate them like this?
I want to separate \frac{1} {12} G_{\mu\nu\rho} G^{\mu\nu\rho} into time and space component . Where G_{\mu\nu\rho}\equiv\partial_{\mu}\phi_{\nu\rho}+ \partial_{\nu}\phi_{\rho\mu}+\partial_{\rho}\phi_{\mu\nu}
How can I do it?
If there are 3 indices how can I separate them like this?
I want to separate \frac{1} {12} G_{\mu\nu\rho} G^{\mu\nu\rho} into time and space component . Where G_{\mu\nu\rho}\equiv\partial_{\mu}\phi_{\nu\rho}+ \partial_{\nu}\phi_{\rho\mu}+\partial_{\rho}\phi_{\mu\nu}
How can I do it?
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