I am following some notes on the computation of the vector two point function in QCD and I would like somebody to make some intermediate steps more explicit. Let's consider

$$\Pi_{\mu\nu}=i\mu^{2\epsilon}\int{}d^dx\,{}e^ {iqx}\langle\Omega|T\{j_{\mu}(x)j_{\nu}(0)\}|\Omega\rangle=(q_{\mu}q_{\nu}-\eta_{\mu\nu}q^2)\Pi,$$

where $\mu$ is a mass scale, $\epsilon$ is the regulator defined in $d=4-2\epsilon$ where $d$ is the dimensionality of space-time and $j_{\mu}(x)=\bar{q}(x)\gamma_{\mu}q(x)$.

The quantity I want to compute is $\Pi$. To do that we first multiply the equation above with $\eta^{\mu\nu}$ on both sides to obtain

$$\Pi=\frac{-i\mu^{2\epsilon}}{(d-1)q^2}\int{}d^dx\,{}e^ {iqx}\langle\Omega|T\{j_{\mu}(x)j^{\mu}(0)\}|\Omega\rangle=\ldots$$

My notes claim that this leads to

$$\ldots=\frac{-iN_c\mu^{2\epsilon}}{(d-1)q^2}\int{}d^dx\,{}e^ {iqx}Tr[S(x)\gamma_{\mu}S(-x)\gamma^{\mu}],$$

where $N_c$ is the number of colors and $S(x)$ is the free quark propagator.

I want somebody to make the steps between the last two equations explicit, particularly I am interested on where do the traces come from.