Resource recommendation for path integral formalism in condensed matter

Question

I am familiar with Green's function and perturbation theory for many-body systems. I have learned this theory from Henrik Bruus's book Many-Body Quantum Theory in Condensed Matter Physics. This book works with operator formalism instead of path-integral formalism.

I am looking for books/articles to learn Green's function perturbation theory based on path-integral formalism. My focus is on condensed matter physics problems, for example, calculating response functions.

Answer 1

As already mentioned by @Meng Cheng in the comments,

• Condensed Matter Field Theory by Altland & Simons is a very well written text which contains what you need.

I list a few more resources below for some variety,

• Quantum Field Theory: Feynman Path Integrals and Diagrammatic Techniques in Condensed Matter by Lukong, is a relatively new but beautifully written book which contains what you're looking for,
• Advanced Quantum Condensed Matter Physics: One-Body, Many-Body, and Topological Perspectives by El-Batanouny, is yet another massive new book that treats green's functions and path integrals in a condensed matter setting,
• Introduction to Many-Body Physics by Coleman is a classic text on many-body theory that deals with these topics as well,
• Quantum Condensed Matter Field Theory is a course taken by Ben Simons at the University of Cambridge, which contains lecture notes that are a condensed version of his and Altland's book,
• QFT I and QFT II are a couple of elegant and concise handwritten lecture notes by Martin Zirnbauer on his courses at the University of Cologne.

Finally, another text you may find useful as an additional reference is,

• Path Integrals: In Quantum Mechanics, Statistics, Polymer Physics and Financial Markets by Hagen Kleinert

It is a comprehensive open source text on path integrals and perhaps one of the only books that explicitly solves them for various non-trivial quantum systems, such as the hydrogen atom.

Hope you find what you're looking for :)

Answer 2

Quantum Many-particle Systems by Negele and Orland is somewhat dated but a classic - for those who prefer solid older books with down-to-earth explanations.