Iterative analytic continuation of the electron self-energy to the real axis

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Abstract
The electron Green’s function in the superconducting state can be solved either at discrete Matsubara frequencies along the imaginary axis, or as a function of a continuous variable along the real frequency axis. The former is considerably more convenient to calculate than the latter. We derive a formally exact analytic continuation of the imaginary-axis solutions to the real frequency axis. The procedure is applicable to more general problems involving Green’s functions. We apply our method to calculating the tunneling density of states for superconducting lead.