  The lepton asymmetry generated by the out-of-equilibrium decays of heavy
Majorana neutrinos with a quasi-degenerate mass spectrum is resonantly
enhanced. In this work, we study this scenario within a first-principle
approach. The quantum field theoretical treatment is applicable for mass
splittings of the order of the width of the Majorana neutrinos, for which the
enhancement is maximally large. The non-equilibrium evolution of the mixing
Majorana neutrino fields is described by a formal analytical solution of the
Kadanoff-Baym equations, that is obtained by neglecting the back-reaction.
Based on this solution, we derive approximate analytical expressions for the
generated asymmetry and compare them to the Boltzmann result. We find that the
resonant enhancement obtained from the Kadanoff-Baym approach is smaller
compared to the Boltzmann approach, due to additional contributions that
describe coherent transitions between the Majorana neutrino species. We also
discuss corrections to the masses and widths of the degenerate pair of Majorana
neutrinos that are relevant for very small mass splitting, and compare the
approximate analytical result for the lepton asymmetry with numerical results.
