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We derive field-theoretic local quantum transport equations which candescribe quantum coherence. Our methods are based on Kadanoff--Baym equationsderived in the Schwinger--Keldysh closed time path formalism of non-equilibriumquantum field theory. We focus on spatially homogeneous and isotropic systemsand mixing fermions with a time-dependent mass and a weak coupling to a thermalplasma.  We introduce a new local approximation (LA) method and use it to derivequantum kinetic equations which can describe coherence and also include effectsof the spectral width. The method is based on a local ansatz of the collisionterm. We also improve the earlier coherent quasiparticle approximation (cQPA)by giving a straightforward derivation of the spectral ansatz, a new way oforganizing the gradient expansion, and a transparent way to derive thecoherence-gradient resummed collision term. In both methods the transportequations can describe flavor coherence and particle--antiparticle coherence,and the related oscillations, of the mixing fermions.  In addition to formulating the local equations we apply them to baryogenesisin the early universe. More specifically, we study the details of CP-asymmetrygeneration in resonant leptogenesis and the evolution of the axial vectorcurrent in electroweak baryogenesis (in a time-dependent analogue). We solvethe equations numerically, and perform extensive analysis and compare theresults to semiclassical (Boltzmann) equations. The results cover knownsemiclassical effects. We find that dynamical treatment of local quantumcoherence is necessary for an accurate description of CP-asymmetry generation.When these details are known they can then be partially incorporated intosimpler (e.g. semiclassical) approaches. However, coherent quantum kineticequations are needed for accurate results across different scenarios or wideparameter ranges.

Quantum coherence in relativistic transport theory: applications to baryogenesis