  The f-electron spectral function of the Falicov-Kimball model is calculated
via a Keldysh-based many-body formalism originally developed by Brandt and
Urbanek. We provide results for both the Bethe lattice and the hypercubic
lattice at half filling. Since the numerical computations are quite sensitive
to the discretization along the Kadanoff-Baym contour and to the maximum cutoff
in time that is employed, we analyze the accuracy of the results using a
variety of different moment sum-rules and spectral formulas. We find that the
f-electron spectral function has interesting temperature dependence becoming a
narrow single-peaked function for small U and developing a gap, with two
broader peaks for large U.
