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I would like to re-open a topic raised by Si in 2003.

I agree with Si that Weinberg's vol.1 is a reference for setting the fundings of QFT, but it lacks explanations between the lines.

I would then suggest to post here the questions everyone has on this book, so that people could bring their answers, and then we could try to compile all these Q&A on this site.

I will start with my current question :

It is related to relations (7.1.17) and (7.1.18) of page 295. These are presented as "definitions" of a quantum mechanical functional derivative. This is consistent with the functional derivative for classical fields based on Poisson brackets, if we considered as granted the equivalence {,} <--> i[,]. But this equivalence is in fact only analyzed in 7.6. If this equivalence is not part of the assumptions, how can we then demonstrate the relation of the top of p.296?

I know of a "demonstration" (in fact considered an "evidence"! of relation (7.1.17) in "Fonda-Ghirardi-"Symmetry principle in quantum physics", page 374. If we could indeed develop F[q(t), p(t)] as a "Taylor expansion" using functional derivatives (I failed doing so), then usual commutation relations between q and p would allow us to obtain (7.1.17), but then why does Weinberg call it a "definition"?