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http://mathoverflow.net/a/21908/69479

I lack the knowledge to do the derivation on my own so I would like to ask for your help. I am an undergraduate.

I do not understand what a "first order differential operator" looks like. Is it just a combination of first order partial derivatives, like [itex]\sum c_i \frac{\partial}{\partial x_i}\vec{e}_i[/itex] ([itex]c_i[/itex] are generic constants)? I do not know either how to check whether my operator commutes with translations and rotations in order to see that "it is a multiple of curl".

If this is submitted to the wrong section I apologize.

Thank you for your time.