Towards a kinetic theory for fermions with quantum coherence

Understand

A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection).

• A central element in our derivation is finding new spectral solutions for the 2-point Green's functions written in the Wigner representation, that are carrying the information of the quantum coherence.
• Physically observable density matrix is then defined from the bare singular 2-point function by convoluting it with the extrenous information about the state of the system.
• The formalism is shown to reproduce familiar results from the Dirac equation approach, like Klein problem and nonlocal reflection from a mass wall.