# How can curl of 4-vector or 6-vector be writen?

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## Main Question or Discussion Point

How can a curl of 4-vector or 6-vector be writen? Let's say that we have a 4-vector A4=(a1,a2,a3,a4)
how can we write in details the ∇×A4

Can we follow the same procedure for 6-vector?

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Orodruin
Staff Emeritus
This construction appears, eg, when considering the electromagnetic field tensor as the exterior derivative of the 4-potential $F = dA$. As you may be aware, the field tensor $F$ has six independent components, three for the electric field and three for the magnetic.