  The theory for time-resolved photoemission spectroscopy as applied to
pump-probe experiments is developed and solved for the generic case of a
strongly correlated material. The formal development incorporates all of the
nonequilibrium effects of the pump pulse and the finite time width of the probe
pulse. While our formal development is completely general, in our numerical
illustration for the Hubbard model, we assume the pump pulse drives the
electrons into a nonequilibrium configuration, which rapidly thermalizes to
create a hot (quasi-equilibrium) electronic system, and we then study the
effects of windowing that arise from the finite width of the probe pulse. We
find sharp features in the spectra are broadened, particularly the
quasiparticle peak of strongly correlated metals at low temperature.
