TIME-DEPENDENT FUNCTIONAL THEORY FOR SUPERCONDUCTORS

We develop a Keldysh-Eliashberg-type formalism based on a functional t heory for strongly correlated inhomogeneous superconductors subject to time-dependent external forces on the ions, four-vector, and pairing potentials. This theory incorporates exchange-correlation effects incl uding a self-consistent treatment of the electromagnetic vector field as well as the ion motion on equal footing. Thus our theory not only c ontains but also goes beyond the scope of a recently published time-de pendent density functional theory for superconductors.