What does $oversetleftrightarrow{partial_{mu}}$ means?

Question

I have a scalar complex field: $phi(x) = phi_{1} + i phi_{2};$ so $;phi^{*}(x) = phi_{1} - i phi_{2}$ where $phi_{1}, ; phi_{2}$ are  real scalar fields.
Then I have something like $;phi^{*}oversetleftrightarrow{partial_{mu}}phi ;$. What does this $;oversetleftrightarrow{partial_{mu}}$ means?
(PS: I Know that $partial_{mu} = frac{partial}{partial x^{mu}}$)

Pipe · Answer

It is just a compact way of saying $$(partial_{mu}phi^{*})phi - (partial_{mu}phi)phi^{*}$$
The double arrow is just to remember that the derivative applies on the field and on the conjugate field.

What does $oversetleftrightarrow{partial_{mu}}$ means?

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