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I am taking a course on Quantum Field Theory where we work alot with the functional derivative.

Does anyone know of a good, free online PDF tutorial with some examples?

Cheers!

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It may be helpful to learn a little functional analysis. In this case the relevant topic is the Gateaux and Frechet derivatives on locally convex topological vector spaces. A lot of the stuff physicists do will make more sense if you learn the math for real instead of in their hand-waving manner. –  Nick Alger Mar 10 '12 at 7:15
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You might want to take a look at following introductions.

Unfortunately I don't know how good they describe functional derivative, figure it out by yourself.

Quantum Field Theory. Mark Srednicki

Quantum Field Theory. Frank Wilczek

Introduction to Quantum Field Theory. Arthur Jaffe

An Introduction to Quantum Field Theory. Mrinal Dasgupta

An Introduction to Quantum Field Theory. Hartmut Wittig

The next list should be more useful I assume

Funcational Methods in Quantum Field Theory. Alex Nelson

Quantum Field Theory II.Dr. Matthias R. Gaberdiel, Dr. Aude Gehrmann-De Ridder

Advanced Quantum Field Theory.Prof. Claudio Scrucca

Hopefully It will be helpfull!

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FMiQFT by Nelson looks promising. Thanks! –  trolle3000 Mar 26 '12 at 12:57
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