Reference for rigorous interacting many-body quantum mechanics

Question

Are there good references for (both zero and finite time) interacting systems of quantum many-body theory? More precisely, I would be interested in references discussing the following topics:

1. Second quantization
2. Zero and finite time Green's function (time-ordered two point function) and its relation to spectra of the full Hamiltonian (i.e. with interacting term)
3. Perturbation theory (e.g. Gellmann and Low formula, Wick's theorem etc)
4. Linear response theory

These are some standard topics in physics books about many-body quantum mechanics. I am basically looking for rigorous justification of (at least some) of the most important formulas in the physics textbooks about these topics using good functional analysis.

Disclaimer: I don't know to what degree the topics above are well-developed from the mathematical point of view. I am assuming one can get pretty far and cover a lot (if not every) topic using functional analysis and related techniques, in the spirit of Reed & Simon.

Answer 1

A textbook that covers much ground in a mathematically rigorous way is Mathematical Methods of Many-Body Quantum Field Theory by Detlef Lehmann (2004).

This book offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams.

Answer 2

I believe all of these topics and more are also covered in

Dereziński, Jan; Gérard, Christian, Mathematics of quantization and quantum fields, Cambridge Monographs on Mathematical Physics. Cambridge: Cambridge University Press (ISBN 978-1-107-01111-3/hbk; 978-0-511-89454-1/ebook). xii, 674 p. (2013). ZBL1271.81004.