The Boltzmann Equation from Quantum Field Theory

TL;DR

This paper derives the classical Boltzmann equation from relativistic quantum field theory using the Kadanoff-Baym equations and the WKB approximation, applicable to far-from-equilibrium and expanding universe scenarios.

Contribution

It provides a first-principles derivation of the Boltzmann equation from quantum field theory, including off-shell transport effects, beyond previous approximate methods.

Findings

Derivation of a generalized Boltzmann equation from quantum field theory.

Validation of the equation in far-from-equilibrium and expanding backgrounds.

Inclusion of off-shell transport phenomena in kinetic equations.

Abstract

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff-Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.