Equivalence of the channel-corrected- T -matrix and anomalous-propagator approaches to condensation

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 nonconservation 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 a chosen approximation in the same way as the coherent-potential approximation improves the averaged $T$ matrix for impurity scattering.