  In this study, current pumping by an external potential is studied on the
basis of the Keldysh Green's function method, and a pumping formula written in
terms of retarded and advanced Green's functions is obtained. It is shown that
pumping is essentially driven by a change of particle distribution before and
after an external perturbation. The formula is used to study the spin pumping
effect in the case of strong sd exchange interaction, and the driving field is
identified to be the spin gauge field. At the lowest order in the precession
frequency of magnetization, the spin gauge field works as a constant potential,
and the system is shown to reduce to a static problem of spin current
generation by a time-independent potential with off-diagonal spin components.
