Beyond the Boltzmann equation for weakly coupled quantum fields

A bstract We study the kinetic theory of a weakly interacting quantum field. Assuming a state that is close to homogeneous and stationary, we derive a closed kinetic equation for the rate of change of the occupation numbers, perturbatively in the coupling. For a dilute gas, this reproduces the quantum Boltzmann equation, which only accounts for two-to-two scattering processes. Our expression goes beyond this, with terms accounting for multi-particle scattering processes, which are higher order in the density.