The Boltzmann equation from quantum field theory
Abstract
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the KadanoffBaym 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 KadanoffBaym 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 offshell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.
 Publication:

Physics Letters B
 Pub Date:
 January 2013
 DOI:
 10.1016/j.physletb.2012.11.046
 arXiv:
 arXiv:1202.1301
 Bibcode:
 2013PhLB..718.1119D
 Keywords:

 High Energy Physics  Phenomenology;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 title changed, discussion extended and example added, references added