Some comments on the time-dependent variation principle

P.‐G. Reinhard

Katsuhisa Ohta

R. Jackiw, Arthur K. Kerman

Giovanni Vignale

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.

Roberto Moccia

Abstract The time‐dependent variational principle due to Frenkel is derived from Hamilton's principle using a suitable general expression for the variational wave function. The connections with a recent comment of P. O. Löwdin and P. K. Mukherjee on the same subject are discussed.