= Solution
{c}
Put $S(p)=i(\not p+m)/(p^2-m^2+i0)$ for the <Dirac propagator>, and $\int_\ell=\mu_R^{2\epsilon}\int d^{4-2\epsilon}\ell/(2\pi)^{4-2\epsilon}$ for a translation-invariant <dimensional regularization> of the <loop momentum> integral. The two oriented <scattering amplitudes> are
$$
\boxed{\begin{aligned}
i\mathcal M_A^{\mu\nu\rho}
&=-\int_\ell\operatorname{tr}\left[
(-ie\gamma^\mu)S(\ell+k_1)
(-ie\gamma^\nu)S(\ell-k_3)
(-ie\gamma^\rho)S(\ell)\right],\\
i\mathcal M_B^{\mu\nu\rho}
&=-\int_\ell\operatorname{tr}\left[
(-ie\gamma^\mu)S(\ell+k_1)
(-ie\gamma^\rho)S(\ell-k_2)
(-ie\gamma^\nu)S(\ell)\right].
\end{aligned}}
$$
The common minus sign is the <closed fermion loop sign>. There is no additional <symmetry factor> for either labelled orientation. Each expression is a <trace> over spinor indices; all external photon <propagators> are amputated. If $K(p)=(\not p+m)/(p^2-m^2+i0)$, the common factor is $-(-ie)^3i^3=-e^3$, so, for example, $i\mathcal M_A=-e^3\int_\ell\operatorname{tr}[\gamma^\mu K(\ell+k_1)\gamma^\nu K(\ell-k_3)\gamma^\rho K(\ell)]$.
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