I am working on second quantization of the Dirac field with discrete momentum I was asked to compute the creation/annihilation anticommutator by imposing the anticommutators on $\psi$ i.e.
$$ \{\psi_a(\vec{x}),\psi^{\dagger}_b(\vec{y})\} = \delta^{(3)}(\vec{x}-\vec{y})\delta_{ab}$$
I start with:
$$\psi(\vec{x}) = \sum_{r,\vec{k}} \sqrt{\dfrac{m}{VE_{\vec{k}}}}\bigg[ c_k(\vec{k})\,u_r(\vec{k}) \,e^{-i x \cdot p} + d^{\dagger}_r(\vec{k})\,v_r(\vec{k})\, e^{ix \cdot p} \bigg] $$
Since I am trying to isolate $c$ and $d$ I try to multiply for the expoencial $e^{ix\cdot p'}$ and integrate over the volume, and I will apear an integral like this
$$\iiint_V e^{-i \,x \cdot (p'-p)} \,d^3x$$
Is there any way approximate this? Like doing:
$$\iiint_V e^{-i \,x \cdot (p'-p)} \,d^3x \approx V\delta_{p,\,p'}$$
