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How are tree-level calculations related to the classical theory?

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I've read the answers (and linked notes) to another question (Tree level QFT and classical fields/particles) and I understand them. They seem to explain how to organise a perturbative calculation of the solution to a classical non-linear ODE by drawing diagrams which look a bit like Feynman diagrams. But it is not clear to me how these diagrams correspond to actual Feynman diagrams. In QFT, when Feynman diagrams are used when doing path integrals (to calculate correlation functions etc.) but not to solve for the fields. What does the tree-level expansion of a correlation function mean and what is its classical interpretation?

This post imported from StackExchange Physics at 2016-05-31 07:24 (UTC), posted by SE-user octopus
asked Oct 22, 2015 in Theoretical Physics by octopus (0 points) [ no revision ]
The question (v2) (including the title question) seems to be essentially a duplicate of the linked Phys.SE question.

This post imported from StackExchange Physics at 2016-05-31 07:24 (UTC), posted by SE-user Qmechanic
The linked question has several answers, one of which is accepted, which don't answer this question (and arguably the other one). Perhaps that's because nobody knows the answer...

This post imported from StackExchange Physics at 2016-05-31 07:24 (UTC), posted by SE-user octopus

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