I am especially interested in the expansion of a 4-vertex which is the sum of 1PI diagrams in the expansion of the 4-point connected correlation function.
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You can just do perturbation theory without drawing diagrams, by taking functional derivatives... What is your question, exactly? – Danu Mar 09 '15 at 08:46
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Can you explain with example of a 4 vertex on how to take functional derivatives and come up with an expansion to 2nd order? – user142341 Mar 09 '15 at 21:38
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This is not really insightful, and it's covered in most books on quantum field theory. Have you looked at any of the standard references? – Danu Mar 10 '15 at 00:09
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I haven't come across a single book on QFT that explicitly derives the 4-point vertex perturbation expansion. Could you cite the references? – user142341 Mar 10 '15 at 02:14
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They may not explicitly carry out your calculation, but the methods are clearly set up in e.g. Ryder, Srednicki. – Danu Mar 10 '15 at 10:15