  The quantum Boltzmann equations relevant for leptogenesis, obtained using
non-equilibrium quantum field theory, are described. They manifest memory
effects leading to a time-dependent CP asymmetry which depends upon the
previous history of the system. This result is particularly relevant in
resonant leptogenesis where the asymmetry is generated by the decays of nearly
mass-degenerate right-handed neutrinos. The impact of the non-trivial time
evolution of the CP asymmetry is discussed either in the generic resonant
leptogenesis scenario or in the more specific Minimal Lepton Flavour Violation
framework. Significant quantitative differences arise with respect to the usual
approach in which the time dependence of the CP asymmetry is neglected.
