[Physics] Self-teaching Green’s function approach to quantum many-body systems

Question

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My question is where can I find a good book, review, online course, or all of them for self-teaching Green's function in quantum many-body problems (if it has problems with solutions for self-evaluating the concepts the better).

As I start to dig in the field, I find very nice books on one-particle green's function (e.g. Economou's book). However, the many-body non-equilibrium Green's function is presented always in a cloud of mysticism understandable only for people in field.

I am acquaintance with one particle Green's function at Sakurai's (scattering) level, but no more than that.

Answer 1

I highly recommend Richard D. Mattuck A Guide to Feynman Diagrams in the Many-Body Problem. You can read some pages here.

It's a very surface level introduction, but the first 3 or so chapters are presented at what he calls a "kindergarten" level so you shouldn't have any problems understanding it. However, the last part is most definitely not "kindergarten".