The Keldysh formalism in the time-dependent density-functional theory

Abstract

We have considered application the Keldysh formalism in time-dependent density functional theory. It is shown that effects of electron-electron interaction can be taken systematically into account in the framework of the Kadanoff-Baym equations for Green functions determined on the Keldysh contour for the second-order 47 self-energy approximation. With the help of these Green functions we have derived the time-dependent Kohn-Sham potential from an action functional. The Keldysh formalism in a similar way leads to response functions that obey the causality principle that is illustrated on the case of the time-dependent optimized effective potential equations.