Conserving T-matrix theory of superconductivity

TL;DR

This paper modifies the T-matrix theory of superconductivity by removing self-interactions, making it applicable to the superconducting state while preserving conservation laws, and connects it to Eliashberg theory.

Contribution

It introduces a self-interaction removal in the T-matrix approximation, extending its applicability to superconductivity without violating conservation principles.

Findings

The corrected theory is equivalent to removing nonphysical repeated collisions.

It remains conserving in the Baym-Kadanoff sense.

The approach leads to a form of Eliashberg theory for a single pairing channel.

Abstract

We remove a self-interaction from the Galitskii-Feynman T-matrix approximation. This correction has no effect in the normal state but makes the theory applicable to the superconducting state. It is shown that identical theory is obtained by removing nonphysical repeated collisions in the spirit of the Fadeev-Watson-Lovelace multiple scattering expansion. Our correction does not violate the two-particle symmetry of the T-matrix, therefore the present theory is conserving in the Baym-Kadanoff sense. The theory is developed for retarded interactions leading to the Eliashberg theory in the approximation of a single pairing channel.