ABSTRACT
In real metals, retardation and damping effects play a strong role in a fundamental understanding of the superconducting phase. If the effective potential is attractive, one would expect to find a bound state of the two-particle system, or instability of the system as a whole. The energy gap in the superconducting state involves the latter quantity, a result which depends on a consistent treatment of correlations both above and below the Fermi surface. For finite-temperature problems one would like to define the one-particle Green's function as the statistical average of Green's functions defined for the exact excited states of the system. The effective density of quasi-particle states in energy is well approximated by the simple BCS model near the edge of the gap with small deviations of order or less than one to five per cent occurring in the vicinity of the Debye frequency.
