Integrating by parts Maxwell Lagrangian

1. Feb 26, 2012

Lapidus

I attached a file that shows the free EM action integral and how it can be rewritten. I would like to know how to go from the first line to the second. I have to integrate by parts somehow, and I know surface terms get thrown out, but I do not know how the indices of the gauge fields should be handled.

thanks for any help

Attached Files:

• integrating by parts.pdf
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2. Feb 28, 2012

Lapidus

Has then perhaps anybody seen a text were it is derived?

I got -A∂∂A + A∂∂A, and both terms upper indices for A∂ and lower indices for ∂A. But what now? How to get to the last line?