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I'm studying quantum field theory and I encountered some problems of diffusion of particles by an external potential. Until now I have to do with diffusion of the type particle-particle obtaining the Feynman rules from the Lagrangian of the theory and I don't know how to implement the presence of an external potential. How can I implement it?

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It's probably better to just ask how to do it, rather than asking for a reference specifically. (Unless there is some reason you need a particular paper or something) – David Zaslavsky♦ Sep 6 '11 at 8:37
I modified the question – Andrea Amoretti Sep 6 '11 at 8:45
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Can you explain the term "diffusion"? You might be translating insccurately to English. Do you mean quantum fields or statistical fields? Do you mean diffusion or quantum propagation (Anderson used to call this diffusion too)? If you mean "what is the quantum propagator in an external potential" the answer is different than "what is the diffusive classical propagation in a thermal bath and external forces". – Ron Maimon Sep 6 '11 at 23:36
In general whenever you ask a question, it is a good idea to let people know what reference you are studying, what reference you encountered some problems, etc, to put your question in the right context, and everybody on the same page... – Qmechanic♦ Oct 7 '11 at 16:24

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Diffusion means scattering, I guess.

The diagram technique exists for external fields too. In QED you write $L_{int} \propto j\cdot A + j\cdot A_{ext}$ and denote $A_{ext}$ as a different from photon line. $A_{ext}$ is a know function of space-time arguments. I saw the corresponding diagrams in many textbooks. You just have to look, for example, at scattering an electron from a nucleus in QED.

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