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.

Langevin description of nonequilibrium quantum fields

“…we write (19) as The equivalence is complete provided the sources are chosen in an appropriate way. For the case of an instantaneous kick,…”

“…The most popular such effective approaches are kinetic descriptions [8,9,[12][13][14][15][16][17][18][19][20], or effective Langevin descriptions [21][22][23][24][25][26][27][28]. A key issue in this context concerns the domain of validity of such approaches.…”

“…backreact, see e.g. [19,40,44]. In more general cases, the influence functional approach of Feynman and Vernon allows one to derive approximate Langevin equations [23,40,47].…”

Curvaton dynamics revisited

“…• The number density of φ particles obeys an equation similar to that of condensation (See [48,49] for instance).…”

Backreaction effects on nonequilibrium spectral function

“…This simple scenario can be used as the starting point to comprehend the properties of the KBE and their relation to the semiclassical Boltzmann equation, where already numerous studies has been performed [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. For example, it was shown in [26] that the main difference between both evolution equations comes from the fact that there is a time where quantum processes are important, time that is related to the decay width of the out-of-equilibrium field.…”