Equivalence of channel-corrected T-matrix and anomalous propagator approach

Any many-body approximation corrected for unphysical repeated collisions in a given condensation channel is shown to provide the same set of equations as they appear by using anomalous propagators. The ad-hoc assumption in the latter theory about non-conservation of particle numbers can be released. In this way the widespread used anomalous propagator approach is given another physical interpretation. A generalized Soven equation follows which improves any approximation in the same way as the coherent potential approximation (CPA) improves the averaged T-matrix for impurity scattering.