Wave function normal modes in 3-torus I'm studying the states of spin-less neutral particles and their Fock space. 
I upload the picture in order to make my question clearer.
Talking about $(N,r)$-improper states, the expectation value of number operator results in products of delta functions and Kronecker deltas (Eq. 3.79). Then, to have a clearer result it says that I can restrict the normal modes to a 3- torus. 
First, I don't think I get the implication of doing so;
Second, why can I restrict the normal modes to the interior of a 3-torus without loss of generality? Why is it a 3-torus?

 A: Flat torus is just the mathematical term for a flat space with periodic boundary conditions. A space-like $3$-torus is therefore three-dimensional ordinary space ("ordinary" meaning "without a time-like direction" here) with periodic boundary conditions, just like the book says :)
You probably think "donut" when you hear the word torus. Imagine cutting such a donut along the lines marked in this picture:

(Source: Wikipedia)
If you take the result and "unroll" it (make it flat), you get a flat rectangle with periodic boundary conditions. That's why this donut is in a topological sense identical to flat two-dimensional space with periodic boundary conditions and this is where the term "$n$-torus" used by mathematicians comes from.
Edit: From your question I assumed that the confusion came from the term "3-torus" used in this way. If not, I'm sorry ;) You can restrict the modes without loss of generality because infinite space is just the limit of a 3-torus where you increase the side length $L$. The implication is that the wave vector $k$ becomes quantized as described in your book.
