- #1
decerto
- 87
- 2
Could someone explain how can one go from
$$ \int dx\ \frac{-1}{4}F^{\mu \nu}F_{\mu \nu}$$
where $$F_{\mu \nu} = \partial_{\mu} \phi_{\nu}-\partial_{\nu} \phi_{\mu}$$
to
$$\int dx\ \frac{-1}{2}(\partial_{\mu} \phi^{\nu})^2 + \frac{1}{2}(\partial_{\mu} \phi^{\mu})^2 $$
I assume it has something to do with integration by parts but I can't see it
$$ \int dx\ \frac{-1}{4}F^{\mu \nu}F_{\mu \nu}$$
where $$F_{\mu \nu} = \partial_{\mu} \phi_{\nu}-\partial_{\nu} \phi_{\mu}$$
to
$$\int dx\ \frac{-1}{2}(\partial_{\mu} \phi^{\nu})^2 + \frac{1}{2}(\partial_{\mu} \phi^{\mu})^2 $$
I assume it has something to do with integration by parts but I can't see it