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A new density matrix and corresponding quantum kinetic equations areintroduced for fermions undergoing coherent evolution either in time (coherentparticle production) or in space (quantum reflection). A central element in ourderivation is finding new spectral solutions for the 2-point Green's functionswritten in the Wigner representation, that are carrying the information of thequantum coherence. Physically observable density matrix is then defined fromthe bare singular 2-point function by convoluting it with the extrenousinformation about the state of the system. The formalism is shown to reproducefamiliar results from the Dirac equation approach, like Klein problem andnonlocal reflection from a mass wall. The notion of the particle number in thepresence of quantum coherence is shown to be particularily transparent in thecurrent picture. We extend the formalism to the case of mixing fields and showhow the usual flavour mixing and oscillation of neutrinos emerges again from asingular shell structure. Finally, we show how the formalism can be extended toinclude decohering interactions.

Towards a kinetic theory for fermions with quantum coherence