Modifying the variational principle in the action integral functional derivation of time-dependent density functional theory

TL;DR

This paper critically analyzes the variational principle used in deriving time-dependent density functional theory (TDDFT), highlighting issues with the original approach and proposing a modification to address fundamental problems in the variational formulation.

Contribution

It offers a critical analysis of the variational principle in TDDFT derivation and discusses the indefiniteness of the action integral functional, proposing modifications to improve the theoretical foundation.

Findings

The original variational principle in TDDFT derivation is flawed.

The indefiniteness of the Runge-Gross action integral functional is a fundamental problem.

Modifications to the variational principle are necessary for a consistent TDDFT framework.

Abstract

According to a recent paper by G. Vignale [Phys. Rev. A 77, 062511 (2008), arXiv:0803.2727], the problems arising in the original derivation of time-dependent density functional theory (TDDFT) based on the Runge-Gross (RG) action-integral functional (AIF) are due to an incorrect variational principle (VP). This argument and the proposed modification of the VP are critically analyzed. The more fundamental problem, though, is the indefiniteness of the RG AIF. In contrast to a widely held belief, that indefiniteness is not eliminated in the variational procedure, which unwittingly is corroborated by Vignale's initial point.