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Integrating by parts Maxwell Lagrangian

  1. Feb 26, 2012 #1
    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:

  2. jcsd
  3. Feb 28, 2012 #2
    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?
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