The Boltzmann Equation from Quantum Field Theory
  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.
