Towards a kinetic theory for fermions with quantum coherence

TL;DR

This paper develops a new quantum kinetic theory for fermions that incorporates quantum coherence, providing a unified framework for phenomena like particle production, reflection, and neutrino oscillations, with potential to include decoherence effects.

Contribution

It introduces a novel density matrix and spectral solutions for fermionic quantum coherence, unifying various phenomena and extending to mixing fields and decoherence within a kinetic theory.

Findings

Reproduces Dirac equation results like Klein problem and reflection.

Clarifies particle number definition amid quantum coherence.

Shows how neutrino oscillations emerge from the formalism.

Abstract

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. The notion of the particle number in the presence of quantum coherence is shown to be particularily transparent in the current picture. We extend the formalism to the case of mixing fields and show how the usual flavour mixing and oscillation of neutrinos emerges again from a singular shell structure. Finally, we show how the formalism can be extended to include decohering interactions.