On the derivation of the Boltzmann equation in quantum field theory: Flat spacetime

Details On the derivation of the Boltzmann equation in quantum field theory: Flat spacetime On the derivation of the Boltzmann equation in quantum field theory: Flat spacetime

2010-03-08

arxiv.org/abs/1003.1621v1

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 52 pages, no figures

Scientific paper

In this paper, we analyze in a mathematically rigorous fashion the validity of the Boltzmann transport equation within quantum field theory. We work within the specific model of a hermitian, scalar field with polynomial self-interaction in two-dimensional Minkowski space. Our main results are as follows: Firstly, that one can obtain a non-perturbative, exact integro-differential equation for the number densities, which we called the pre-Boltzmann equation. We secondly take the long-time-dilute-medium limit of this equation, to obtain a simpler equation. This limiting equation is qualitatively similar to the Boltzmann equation, but it involves additional re-scattering terms. These terms disappear if perform a perturbation expansion in the coupling constant and ignore the loop corrections (Born approximation). If loop corrections are included, then we argue that for consistency, one must also keep corresponding rescattering terms which are normally ignored. Our analysis is hence of potential relevance for physical applications of the Boltzmann equation wherein loop effects are essential, such as in the standard scenario of baryogensis in the Early Universe. Our analysis is performed in the context of flat spacetime, but in such a way that the main ingredients can be transferred, straightforwardly to the case of a curved spacetime of Robertson-Walker-type. Our main technical tools are methods from constructive quantum field theory, as well as a general method called "projection technique". This turns out to give convergent expansions, and a rather elegant way of organizing the combinatorics of the various quantum field theoretic expansions in the analysis.

Affiliated with

Also associated with

No associations

Rating

On the derivation of the Boltzmann equation in quantum field theory: Flat spacetime does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the derivation of the Boltzmann equation in quantum field theory: Flat spacetime, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the derivation of the Boltzmann equation in quantum field theory: Flat spacetime will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-677195