Could someone help me understand the reduced $T$-matrix mentioned in Itzykson and Zuber, eq.
$$\langle{f}| T|p_1p_2\rangle=(2\pi)^4\delta^4(P_f-p_1-p_2)\langle f|\mathcal{T}|p_1p_2\rangle. \tag{5-7}$$
How is it possible to extract the delta function?
One way to say it is that total 4-momentum conservation $$ (P_f^{\mu}-p_1^{\mu}-p_2^{\mu})\langle{f}| T|p_1p_2\rangle~=~0, \qquad \mu~\in~\{0,1,2,3\}, $$ implies that the $T$-matrix element $$\langle{f}| T|p_1p_2\rangle\quad\propto\quad\delta^4(P_f-p_1-p_2)$$ is proportional to a 4D Dirac delta distribution.
