I EM Lagrangian: Question on $(\partial_\mu A^\mu)^2$ Term

[-marko-]

The EM Lagrangian is
$$\mathcal{L} = -\frac{1}{2}[(\partial_\mu A_\nu)(\partial^\mu A^\nu) - (\partial_\mu A_\nu)(\partial^\nu A^\mu)]$$

In the QFT notes from Tong the EM Lagrangian is written in the form
$$\mathcal{L} = -\frac{1}{2}[(\partial_\mu A_\nu)(\partial^\mu A^\nu) - (\partial_\mu A^\mu)^2]$$

I don't see how did he get $(\partial_\mu A^\mu)^2$ term? Thanks :)

 

[Orodruin]

Integration by parts. What is relevant is not the Lagrangian density, but the action.

 

[-marko-]

Integration by parts. What is relevant is not the Lagrangian density, but the action.

Many thanks, it's clear now.