I have been asked to take the Fourier transform of the two-point EM current function $$G_{\mu \nu}(x) = \langle \Omega \lvert T\{J_{\mu}(x) J_{\nu}(0) \} \rvert \Omega \rangle,$$ and to prove something specific about said result.
However, I'm having trouble with the following. Should I calculate $$\langle \Omega \lvert T\{J_{\mu}(x) J_{\nu}(0) \} \rvert \Omega \rangle =\frac{\int \mathcal{D}\psi \mathcal{D}\bar{\psi} J_{\mu}(x) J_{\nu}(0) e^{iS[\psi, \bar{\psi}]}}{\int \mathcal{D}\psi \mathcal{D}\bar{\psi} e^{iS[\psi, \bar{\psi}]}},$$ or is there a better approach? I'm aware that the vacuum expectation value could also be computed by taking the functional derivative of the generating functional, but said derivatives are to be taken with respect to the sources, and I'm not sure if in that case I should take the functional derivative with respect to the fields $A_{\mu}(x)$ and $A_{\nu}(0)$.
Any help would be much appreciated.