  A theoretical frame for pump-probe photoemission is presented. The approach
is based on a general formulation using the Keldysh formalism for the lesser
Green's function to describe the real-time evolution of the electronic degrees
of freedom in the initial state after a strong pump pulse that drives the
system out of equilibrium. The final state is represented by a time-reversed
low-energy electron diffraction state. Our one-step description is related to
Pendry's original formulation of the photoemission process as close as
possible. The formalism allows for a quantitative calculation of time-dependent
photocurrent for simple metals where a picture of effectively independent
electrons is assumed as reliable. The theory is worked out for valence- and
core-electron excitations. It comprises the study of different relativistic
effects as a function of the pump-probe delay.
