Keldysh action of a multiterminal time-dependent scatterer

We present a derivation of the Keldysh action of a general multichannel time-dependent scatterer in the context of the Landauer-Buttiker 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's 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.