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 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.
- 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
- E-Print:
- title changed, discussion extended and example added, references added