Classical Boltzmann equation and high-temperature QED

TL;DR

This paper explores the connection between the Boltzmann transport equation and high-temperature quantum electrodynamics, showing their equivalence through thermal Green's functions and forward scattering amplitudes.

Contribution

It demonstrates the equivalence between the collisionless Boltzmann equation and the high-temperature limit of QED using Green's functions and scattering amplitudes.

Findings

The leading high-temperature limit of QED can be derived from the Boltzmann equation.

Explicit examples confirm the theoretical equivalence.

The approach employs forward scattering amplitudes to relate Green's functions and transport equations.

Abstract

The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of quantum electrodynamics. We compare the contributions obtained from the collisionless transport equation with the high temperature limit of the one-loop thermal Green's function. Our approach employs the representation of the thermal Green's functions in terms of forward scattering amplitudes. The general structure of these amplitudes clearly indicates that the physics described by the leading high temperature limit of quantum electrodynamics can be obtained from the Boltzmann transport equation. We also present some explicit examples of this interesting equivalence.