We study the phase space structure of exact quantum Wightman functions in spatially homogeneous, temporally varying systems. In addition to the usual mass shells, the Wightman functions display additional coherence shells around zero frequency k 0 = 0, which carry the information of the local quantum coherence of particle-antiparticle pairs. We find also other structures, which encode non-local correlations in time, and discuss their role and decoherence. We give a simple derivation of the cQPA formalism, a set of quantum transport equations, that can be used to study interacting systems including the local quantum coherence. We compute quantum currents created by a temporal change in a particle's mass, comparing the exact Wightman function approach, the cQPA and the semiclassical methods. We find that the semiclassical approximation, which is fully encompassed by the cQPA, works surprisingly well even for very sharp temporal features. This is encouraging for the application of semiclassical methods in electroweak baryogenesis with strong phase transitions.
We derive non-equilibrium quantum transport equations for flavour-mixing fermions. We develop the formalism mostly in the context of resonant leptogenesis with two mixing Majorana fermions and one lepton flavour, but our master equations are valid more generally in homogeneous and isotropic systems. We give a hierarchy of quantum kinetic equations, valid at different approximations, that can accommodate helicity and arbitrary mass differences. In the mass-degenerate limit the equations take the familiar form of density matrix equations. We also derive the semiclassical Boltzmann limit of our equations, including the CP-violating source, whose regulator corresponds to the flavour coherence damping rate. Boltzmann equations are accurate and insensitive to the particular form of the regulator in the weakly resonant case ∆m » Γ, but for ∆m ≲ Γ they are qualitatively correct at best, and their accuracy crucially depends on the form of the CP-violating source.
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