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I am familiar with the basic ideas of quantum field theory but I feel uncomfortable when I have to derive Feynman rules by myself for a given action (for example in non-linear sigma models or electrodynamics). Could you provide a list of good books, articles, lecture notes and/or any other sources (except Peskin), where Wick's theorem and the Feynman rules are derived from the functional integral in detail, preferably with examples?

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If you'd prefer a more systematic approach using the path integral for gauge theories, I suggest you research the Faddeev-Popov method. A good source to start you off is Srednicki's textbook. –  JamalS Apr 9 at 18:53
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See perimeterscholars.org/home.html, course: Quantum Field Theory II, from 11/12 to 13/14 for a treatment of the path integral. The last lectures of the course focus on the Faddeev-Popov approach. –  JamalS Apr 9 at 18:57
    
Related: physics.stackexchange.com/q/8441/2451 and links therein. –  Qmechanic Apr 9 at 20:35

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