  We present a rigorous solution of the Boltzmann equation for the
electron-phonon scattering problem in three spatial dimensions in the limit of
low temperatures. The different temperature scaling of the various scattering
rates turns the temperature into a control parameter that is not available in
classical kinetic theory and allows for a rigorous proof of Bloch's $T^5$ law.
The relation between the Boltzmann equation and the Kubo formula is also
discussed, as well as implications for the scattering of electrons by
excitations other than phonons.
