The dynamics of fermionic systems at high density can be described by Hartree-Fock theory.
At positive temperature, typical initial data are quasifree mixed states (e.g. Gibbs state).
I will explain how the Araki-Wyss representation can be used to treat the positive temperature
setting by methods first developed for zero temperature, and use it to give a rigorous
derivation of the Hartree-Fock equations for mixed initial data.