  We present a derivation of the Keldysh action of a general multi-channel
time-dependent scatterer in the context of the Landauer-B\"uttiker approach.
The action is a convenient building block in the theory of quantum transport.
This action is shown to take a compact form that only involves the scattering
matrix and reservoir Green functions. We derive two special cases of the
general result, one valid when reservoirs are characterized by well-defined
filling factors, the other when the scatterer connects two reservoirs. We
illustrate its use by considering Full Counting Statistics and the Fermi Edge
Singularity.

Mesoscale and Nanoscale Physics