Quantum kinetic theory for fermions in temporally varying backrounds

TL;DR

This paper develops quantum kinetic equations for fermions in time-dependent backgrounds, incorporating decoherence and collisions, with applications to early universe particle production and thermalization.

Contribution

It introduces a new spectral solution framework for quantum coherence in fermionic systems with time-dependent backgrounds, extending kinetic theory.

Findings

Spectral solutions reveal quantum coherence effects.

Collisions induce smooth decoherence.

Application to particle production during inflation preheating.

Abstract

We derive quantum kinetic equations for fermions in a homogeneous time-dependent background in presence of decohering collisions, by use of the Schwinger-Keldysh CTP-formalism. The quantum coherence (between particles and antiparticles) is found to arise from new spectral solutions for the dynamical 2-point correlation function in the mean field limit. The physical density matrix $\rho$ and its dynamics is shown to be necessarily dependent on the extrenous information on the system, and expressions that relate $\rho$ to fundamental coherence functions and fermionic particle and antiparticle numbers are derived. For an interacting system we demonstrate how smooth decoherence effects are induced by collisions. As special applications we study the production of unstable particles during the preheating stage of the inflation and an evolution of an initially quantum $\rho$ towards a statistical limit including decoherence and thermalisation.