Conserving T-matrix theory of superconductivity

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.