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## Rank 3 tensor created by taking the derivative of electromagnetic field tensor

1. The problem statement, all variables and given/known data

Show that the rank 3 tensor $$S_{\alpha \beta \gamma}=F_{\alpha \beta , \gamma} + F_{\beta \gamma , \alpha} + F_{\gamma \alpha , \beta}$$ is completely antisymmetric.

I just don't feel comfortable doing this stuff at all. Each of the three terms seems like they should be exactly the same to me. Could someone show me how I would start doing something like this please? Furthermore, if this is a rank 3 tensor, what would it mean if this tensor equals 0?

Thanks. :-\
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 Recognitions: Homework Help If $S_{\alpha\beta\gamma}$ is completely antisymmetric, then $$S_{\alpha\beta\gamma}=-S_{\alpha\gamma\beta}$$ $$S_{\alpha\beta\gamma}=-S_{\beta\alpha\gamma}$$ and $$S_{\alpha\beta\gamma}=-S_{\gamma\beta\alpha}$$ That is, $S_{\alpha\beta\gamma}$ is antisymmetric on all pairs of indices.... So, start by comparing $S_{\alpha\beta\gamma}$ to $S_{\alpha\gamma\beta}$ using the definition you posted...