Suppose we have a hypothetical system in which the proper self-energy has the
form \(\Sigma(k, \omega) \approx A \omega+i \operatorname{sgn}(\mu-\omega)
B(\omega-\mu)^{2}\), with \(B>0, A<0\), near the Fermi surface, where \(\mu\) is
assumed known. Find the form of the propagator. What is the discontinuity at
the Fermi surface?
