Comment on "Modifying the variational principle in the action integral functional derivation of time-dependent density functional theory" by Jochen Schirmer [arXiv:1010.4223]

TL;DR

This paper defends the foundations of time-dependent density functional theory against recent criticism, clarifying misunderstandings about the variational principle, causality, and functionals to reaffirm its validity.

Contribution

The author clarifies misconceptions about the variational principle and causality in time-dependent density functional theory, reaffirming its theoretical foundations.

Findings

Criticism is based on misunderstandings of functionals and gauge transformations.

The causality paradox can be resolved through proper reformulation.

The foundational principles of TDDFT remain valid.

Abstract

In a paper recently published in Phys. Rev. A [arXiv:1010.4223], Schirmer has criticized an earlier work of mine [arXiv:0803.2727], as well as the foundations of time-dependent density functional theory. In Ref.[2], I showed that the so-called "causality paradox" - i.e., the failure of the exchange-correlation potential derived from the Runge-Gross time-dependent variational principle to satisfy causality requirements - can be solved by a careful reformulation of that variational principle. Fortunately, the criticism presented in Ref.[1] is based on elementary misunderstandings of the nature of functionals, gauge transformations, and the time-dependent variational principle. In this Comment I wish to point out and clear these misunderstandings.