Cutting rules on a cylinder: a bottom-up approach to quantum kinetic theory for the early universe

TL;DR

This paper introduces a novel method for calculating thermal corrections in quantum kinetic theory relevant to the early universe, using zero-temperature quantum field theory and diagram cutting rules.

Contribution

It develops a bottom-up approach based on cutting rules on a cylindrical surface, providing an alternative to traditional nonequilibrium quantum field theory methods.

Findings

Derives rules for thermal corrections from forward diagram cuts.

Shows equivalence to cutting closed diagrams on a cylinder.

Provides a new framework for early universe quantum kinetics.

Abstract

Nonequilibrium quantum field theory is often used to derive an approximation for the evolution of number densities and asymmetries in astroparticle models when a more precise treatment of quantum thermal effects is required. This work presents an alternative framework using the zero-temperature quantum field theory, $S$-matrix unitarity, and classical Boltzmann equation as starting points leading to a set of rules for calculations of thermal corrections to reaction rates. Statistical factors due to on-shell intermediate states are obtained from the cuts of forward diagrams with multiple spectator lines. It turns out that it is equivalent to cutting closed diagrams on a cylindrical surface.