On the "Causality Paradox" of Time-Dependent Density Functional Theory

TL;DR

This paper resolves the causality paradox in time-dependent density functional theory by reformulating the variational principle, leading to a new expression for the exchange-correlation kernel and validating previous symmetry-based results.

Contribution

It introduces a correct variational formulation for TDDFT, resolving the causality paradox and deriving a new expression for the exchange-correlation kernel in terms of Berry curvature.

Findings

Resolves the causality paradox in TDDFT

Derives a new expression for the exchange-correlation kernel

Validates previous symmetry-based results

Abstract

I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to a new expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the new formulation.