There are at least two ways to compute the electron-self energy. You can use Pauli-Villars or dimensional regularization, for example.
On Weinberg's book, it's chosen the first method, while on my lectures note the second.
My question is: in general, after adding the Pauli-Villars regulator, can I extend the dimension of the integral to $d$-dimensions? I've done the calculations in this way and I got the same result.
Is it correct?