  Flavour effects play an important role in the statistical evolution of
particle number densities in several particle physics phenomena. We present a
fully flavour-covariant formalism for transport phenomena, in order to
consistently capture all flavour effects in the system. We explicitly study the
scenario of Resonant Leptogenesis (RL), and show that flavour covariance
requires one to consider generically off-diagonal number densities, rank-4 rate
tensors in flavour space, and non-trivial generalization of the discrete
symmetries C, P and T. The flavour-covariant transport equations, obtained in
our semi-classical framework, describe the effects of three relevant physical
phenomena: coherent heavy-neutrino oscillations, quantum decoherence in the
charged-lepton sector, and resonant CP violation due to heavy-neutrino mixing.
We show quantitatively that the final asymmetry is enhanced by up to an order
of magnitude, for electroweak-scale heavy neutrinos, as compared to that
obtained from flavour-diagonal or partially flavour off-diagonal equations. A
full field-theoretic treatment in the weakly-resonant regime, based on the
Kadanoff-Baym (KB) equations, confirms that heavy-neutrino oscillations and
mixing are two distinct phenomena, and reproduces the results obtained in our
semi-classical framework. Finally, we show that the quasi-particle ansaetze,
often employed in KB approaches to RL, discard the phenomenon of mixing,
capturing only oscillations and leading to an underestimate of the final
asymmetry by a factor of order 2.
