On the quantum Boltzmann equation

In this contribution I describe the problem of deriving a Boltzmann equation for a system of N interacting quantum particles under suitable scaling limits. From a rigorous viewpoint, the problem is still open and only partial results are available, even for short times. The present report is based on a systematic collaboration with D. Benedetto, F. Castella and R. Esposito: possible mistakes and inconsistencies are however the responsibility of the author.