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:
- Second quantization
- 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)
- Perturbation theory (e.g. Gellmann and Low formula, Wick's theorem etc)
- 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.