Proper mathematical treatments anywhere?

[Cinquero]

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.

 

[dextercioby]

I think J.R.Taylor [1] wrote the kind of book you need for 1).If you like a more mathematical approach,then help yourself with the 3-rd volume of Reed & Simon [2].

The second part is standard,i'm sure of it.I could do it for you from the top of my head,just name the spin of field...Did you try to look for it in P & S or Bailin & Love?

Daniel.

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[1]J.R.Taylor,"Scattering Theory",J.Wiley,1972.
[2] M.Reed,B.Simon,"Methods of Mathematical Physics:Scattering Theory",VOL III,A.P.,1979.

 

[Cinquero]

Who are P & S?

 

[dextercioby]

Peskin & Schroeder,who else...?We're pretty accustomed to using acronyms for book authors,and sometimes even for books...

Daniel.

 

[Cinquero]

Peskin & Schroeder,who else...?

Of course. I was just somewhat confused by the fact that Amazon lists this book under Peskin, but not Schroeder...

P&S: they do the same thing as Zee does: they calculate things on a lattice and then take the continuum limes. It would be no problem for me to accept that as a rule of operation if they would not call it "functional integration" because I don't know of ANY mathematical definition of a functional integral... for example, I have some doubt that the measure for function spaces is in any way uniquely determined. I wonder if it is not an incident that the functional integration approach to perturbation theory works out good, may be an incident due to a symmetry in the functional variations of the Lagrangian in function space. Maybe we can't do perturbation theory for heavily perturbed systems because such systems heavily deviate from that symmetry.

Furthermore, the books of Reed and Simon look just great -- partly because I have nowhere found the notion of an operator-valued Green's function.

Sadly, I had no chance to have a look at the other two books, yet. Maybe tomorrow.

Thx a lot!