Main Question or Discussion Point
What kind of background do I need to study many-body quantum field theory?
Oh... right. That is is even another vector of confusion. Many-body theories can still be interacting (primarily dealing with particles interacting with each other via some two- or three, or more-particle forces) and non-interacting (primarily dealing with free particles, possibly interacting via symmetries (Fermionic/bosinic) and maybe a common one-body external potential).As I understand it, "many-body" and "quantum field theory" are redundant, in the sense that quantum field theory is already inherently a many-body theory. (It's not quite true the other way around--you can do many-body quantum mechanics without field theory.)