A theoretical frame for pump-probe photoemission is presented. The approach is based on a general formulation using the Keldysh formalism for the lesser Greens 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 Pendrys 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.
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