Infinite volume limit literature?

[DrFaustus]

Hey everybody,

I'm currently struggling to make sense of the infinite volume limit of a QFT. What I'm talking about is the (formal) limit of "quantization in a box with periodic boundary conditions" to "quantization in Minkowski space" as the side of the box goes to infinity. Does anyone know of an article or book where this approach is taken? Possibly where the actual formal limit is discussed. No just "And as we take the infinite volume limit we obtain the continuum representation of the operators." but possibly where the various replacements are discussed (sums -> integrals, discrete variables -> continuum variables and so on) more carefully?

Thanks!

 

[Haelfix]

I have that more precisely as lecture notes, but you often see it treated in a kind of roundabout, handwavey way when deriving the path integral and often in lattice theory primers.

Indeed there are a lot of sublteties depending on exactly what you are looking for, and afaik you can take basically take two roads.

The lattice road (alla Wilson) or the more intricate mathematical physics road (see eg Jaffe and people like that)

My guess is probably a lattice theory textbook is your best bet.

 

[DrFaustus]

Haelfix -> Actually I really had Glimm & Jaffe at the back of mind when asking the question. Thing is, their literature is HUGE, and the only paper I have that deals with the infinite volume limit does not address these technicalities. They cite 3 other references: Jaffe's PhD thesis and two proceedings from random conferences, i.e. almost impossible to obtain and surely not quickly. If you have any kind of reference in this sense it'd help a lot!

 

[Bob_for_short]

What do you expect to gain from it? What a particular problem can be related to it?