2
$\begingroup$

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.

$\endgroup$
1
  • 1
    $\begingroup$ Providing a modern and very pedagogical exposition: Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction by Gianluca Stefanucci and Robert van Leeuwen A recent and well written text on advanced condensed matter theory: Introduction to Many-Body Physics by Piers Coleman $\endgroup$ Commented Nov 25, 2021 at 22:48

2 Answers 2

2
$\begingroup$

There are many resources on many-body Green's functions (propagators) both on-line and in print. You may want to search "quantum field methods in many-particle systems" or "quantum field methods for condensed matter systems" or variations thereof.

In any case, I personally recommend the oldie-but-goodie book by Fetter and Walecka, Quantum Theory of Many-Particle Systems. It assumes a good footing in Quantum Theory and Statistical Mechanics, but otherwise covers everything you need for a good handle on the field's basic methods, starting with second quantization and up to finite-temperature and real-time Green's functions. It also includes problems. A Dover edition on Amazon sells for about $21 (new), but I found an on-line copy here:

Fetter and Walecka, Quantum Theory of Many-Particle Systems

Other books available on-line, last one I didn't use directly, but all cover the basics in good detail:

H.Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets. Chap.2 covers the Field Formulation of Many-Body Quantum Physics pretty thoroughly, good intro.

Through the Mueller Group course site at Cornell, Basic Training in Condensed Matter Physics/Many Body Field Theory (unfortunately it seems it is no longer properly maintained since not all links check out anymore; listing only the two working ones for intro material):

Brouwer, Theory of Many-Particle Systems

Nayak, Quantum Condensed Matter Physics

Also check their good list of in-print resources.

$\endgroup$
2
$\begingroup$

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".

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.