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

## TL;DR

This paper demonstrates the equivalence between the channel-corrected T-matrix approach and the anomalous propagator method, providing a new physical interpretation and a generalized Soven equation for improved many-body approximations.

## Contribution

It shows the equivalence of two theoretical approaches and introduces a generalized Soven equation to enhance approximation methods in many-body physics.

## Key findings

- Equivalence between channel-corrected T-matrix and anomalous propagator approaches.
- Reinterpretation of the anomalous propagator method without non-conservation assumptions.
- Introduction of a generalized Soven equation for improved approximations.

## Abstract

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.