I'm looking for proper mathematical treatments of: 1.) Formal (non-relativistic) scattering theory: construction of Moller operators from operator-valued Green's functions. How are these Green's functions defined? What's their exact use and interpretation? Why are there two of them? 2.) Derivation of the free propagator as the inverse of a differential operator. Zee derives in his book "QFT in a Nutshell" that quantity by looking at discretized fields and taking the continuum limes. Isn't there a proper derivation within the framework of functional analysis? Could someone please give me some references at physics books covering such topics in a very rigorous and elegant mathematical manner, ie. in the form of definitions and theorems? I can't stand any more that notoriously bad habit of most physics authors to do all calculations without mentioning even the simplest mathematical theorems.