Relations between action integral, response functions, and causality in density functional theory

Abstract

We consider the standard action functional and show that it is useful in calculating the response functions. It is demonstrated that the response functions obtained from the action integral are the noncausal response functions of a system, while they possess the same information about the excited states as the causal response functions. A paradox related to the causality and symmetry properties of the response functions and the effective interaction is clarified. The connection between the action integral, single-particle potential, response functions, and the effective interaction is elucidated. As a result, a new scheme to construct both the single-particle time-dependent potential and approximations to it is suggested.