Hello! I'm reading up on Hamiltonian mechanics and i stumbled on the fact that the curl of the vector potential can be expressed as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]B_k = \sum_k \epsilon_{kij}\frac{\partial A_i}{\partial x_j}[/tex]

Now the text that I'm reading says that this formula can be inverted as

[tex] \sum_k \epsilon_{kij} B_k = \frac{\partial A_j}{\partial x_i} - \frac{\partial A_i}{\partial x_j}[/tex]

But I then wondered how this inversion would be accomplished?

I suspect the formula [tex]\sum_k \epsilon_{kij} \epsilon_{klm}= \delta_{il}\delta_{jm} - \delta_{im}\delta_{jl}[/tex] to be involved.

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# Inversion of curl of A formula

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