I know that $A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$
But how can write $E_{[a} F_{bc]}$ like the above?
Can you provide a reference where this notational matter is discussed?
Answer
I use following method:
$T_{[ijk]}$
Set indices into determinant
$\left| \begin{matrix} i & j & k \\i & j & k \\i & j & k \end{matrix} \right| = ijk + jki + kij - ikj - jik - kji.$
Next, apply 6 indices and sign into $T$, so we get
$T_{[ijk]} = \dfrac{1}{3!} (T_{ijk}+T_{jki}+T_{kij}-T_{ikj}-T_{jik}-T_{kji}).$
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