I'm studying the proof for the decoherence of the off diagonal elements of a density matrix through scattering with the environment and I'm stuck at a certain point:
My problem is A1.14 relation. (A1.13 as well to be honest, but I guess that the $(2\pi/L)^3$ is just sort of a normalization where $2\pi$ is, maybe $2\pi\hbar$ from the uncertainty relation and $L^3$ is the "volume of the scattering") Sadly I have no idea why $\delta^2(q-q')=\delta(q-q')L$. Oh, $q$ should be a generic module of a momentum (maybe before the scattering) and $q'$ should be the module associated to the momentum of the particle after the scattering.
Since both these relations are said to be "usual replacements" I hope somebody recognise them and can help me out.