A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field

Sébastien Breteaux

Published 2011-07-05, updated 2012-06-25Version 2

In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.