F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach

We derive an alternative representation for the f-electron spectral function of the Falicov-Kimball model from the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted to the real time axis, allowing us to go to arbitrarily low temperatures. The general formula for the retarded Green’s function involves two determinants of continuous matrix operators that have the Toeplitz form. By em