I am reading Schwartz QFT. On page 61 in eq (5.20) he gives an expression that describes the probability for a $2\to n$ scattering event to happen:
$$dP=\frac{T}{V}\frac{1}{(2E_1)(2 E_2)}\left|\mathcal{M}\right|^2 \, d\Pi_{\rm LIPS}\tag{5.20}$$
where $T$ and $V$ are finite time and space volumes and
$$d\Pi_{\rm LIPS}=(2\pi)^4\delta^{(4)}\left(p_1+p_2-\sum_{i=1...n}p_i\right)\times \prod_{i=1...n}\frac{d^3p_i}{(2\pi)^3}\frac{1}{2E_i}.\tag{5.21}$$
Now I consider the example for a $2\to 1$ event. Writing everything out yields:
$$dP=\frac{T}{V}\frac{1}{(2E_1)(2 E_2)(2E_f)}\left|\mathcal{M}\right|^2 \, (2\pi)\delta^{(4)}\left(p_1+p_2-p_f\right)d^3p_f$$
where $p_f$ is the final state momentum. Performing the integral over $p_f$ gives:
$$P=\frac{T}{V}\frac{1}{(2E_1)(2 E_2)(2E_f)}\left|\mathcal{M}\right|^2 \, (2\pi)\delta^{(1)}\left(E_1+E_2-E_f\right)$$
with $E_f=\sqrt{E_1^2+E_2^2}$. I am confused that in this expressions $T$ and $V$ still appear. My feeling tells me that they should drop out since one takes the limit $t,V\to \infty$ in the end.
