Lagrangian of the EM field -- question

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-marko-
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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 :)
 

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  • #2
Orodruin
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Integration by parts. What is relevant is not the Lagrangian density, but the action.
 
  • #3
-marko-
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Integration by parts. What is relevant is not the Lagrangian density, but the action.
Many thanks, it's clear now.
 

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