# According to (4.8.15) in Section 4.8, the scattering rate for fermions is proportional to 1/2 (U D

## Question:

According to (4.8.15) in Section 4.8, the scattering rate for fermions is proportional to 1/2 (U_{D} − U_{E})^{2}, where UD is the direct interaction vertex and U_{E} is the exchange vertex. In the diagram shown in Figure 8.32, only the direct term proportional to U^{2}_{D} occurs. Show that if you account for exchange (how many additional diagrams are needed?), you get agreement of the Matusbara imaginary self energy with the out-scattering rate of (4.8.15).

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