  Thermal leptogenesis explains the observed matter-antimatter asymmetry of the
universe in terms of neutrino masses, consistent with neutrino oscillation
experiments. We present a full quantum mechanical calculation of the generated
lepton asymmetry based on Kadanoff-Baym equations. Origin of the asymmetry is
the departure from equilibrium of the statistical propagator of the heavy
Majorana neutrino, together with CP violating couplings. The lepton asymmetry
is calculated directly in terms of Green's functions without referring to
"number densities". Compared to Boltzmann and quantum Boltzmann equations, the
crucial difference are memory effects, rapid oscillations much faster than the
heavy neutrino equilibration time. These oscillations strongly suppress the
generated lepton asymmetry, unless the standard model gauge interactions, which
cause thermal damping, are properly taken into account. We find that these
damping effects essentially compensate the enhancement due to quantum
statistical factors, so that finally the conventional Boltzmann equations again
provide rather accurate predictions for the lepton asymmetry.
