We have a system of \(N\) non-interacting Fermi particles. (a) They are acted
upon by an external perturbing potential such that \(V_{k t}=A\) for all \(k\), l.
Find the propagator \(G^{+}(\mathbf{q}, \mathbf{p}, \omega), p>k_{r}, q>k_{r}\),
by summing exactly over all diagrams. (b) Generalize your result to the case
where \(V_{k t}\) has the form: \(V_{\mathrm{AI}}=A f_{4} f_{1}\) (factorizable
potential).
