Use the finite-temperature Green’s functions method of this section to compute the diagram shown in Figure 8.32, used in the Fermi liquid theory at the end of this chapter. Show that the result for the imaginary self-energy has the same two terms as in (8.15.17), which are also the same as the rates found by the quantum Boltzmann equation for two-body scattering of fermions.

Transcribed Image Text:

- NF (Ep − µ)(1 — NƑ(Eq_k − µ))(1 — NƑ(Ep+k − µ)) - + NF (Eq_k − μ)NF (Ep+q — µ)(1 — NF (Ez — µ)). - (8.15.17)