Many body interacting fermions problems are formulated in the many body perturbation theory language using Feynman diagrams and imaginary time formalism. To the best of my knowledge the kinetic energy should be the energy of the non interacting system and any correction coming from the interaction would come as self energy corrections. In practical we rarely take the dispersion of the free electrons., it is in general a better to take the DFT dispersion. What is very confusing is that DFT already takes some of the interaction into account, so if i am to use the DFT dispersion in a many body perturbative theory, what should i take for the interaction ?
I understand how can DFT get the dispersion, and i understand how the dispersion is modified by the self energy in MBPT. What i don't understand, is what does it mean to mix both approaches.