Conserving T-matrix theory of superconductivity

A selfconsistent T-matrix theory of many-Fermion systems is proposed. In the normal state the theory agrees with the Galitskii-Feynmann approximation, in the superconducting state it has the form of the renormalized Kadanoff-Martin approximation. The two-particle propagator satisfies the Baym-Kadanoff symmetry condition which guarantees that the theory conserves the number of particles, momentum and energy. The theory is developed for retarded interactions leading to the Eliashberg theory in the approximation of a single pairing channel.