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$\begingroup$ Can you elaborate the expansion? Is the usual expression for the derivative of an exponential not valid for matrix exponentials? $\endgroup$
– gbaso
Commented Jan 11, 2013 at 22:32
$\begingroup$ @Ganondolf see the update. $\endgroup$
– kηives
Commented Jan 11, 2013 at 23:18
$\begingroup$ Uhm, I think I sorted out... Most probably I missed a commutator in the interaction term, which accounts for an extra term in the transformation of G. More important, as you suggested I should keep everything to first order, that should be the way to transform correctly the field strength tensor. I still don't know how exactly, but now I should be on the right way... Dropping the problem now for lack of time, but at least I saw the light at the end of the tunnel. Thank you. $\endgroup$
– gbaso
Commented Jan 12, 2013 at 0:32

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