Time-dependent Kohn-Sham approach to quantum electrodynamics

TL;DR

This paper extends the time-dependent Kohn-Sham framework to quantum electrodynamics, establishing foundational theorems and resolving causality issues in coupled matter-photon systems.

Contribution

It generalizes the van Leeuwen theorem to QED, providing a rigorous basis for a Kohn-Sham approach in quantum electrodynamics.

Findings

Proves the generalized van Leeuwen theorem for QED

Establishes unique effective potentials and currents in the Kohn-Sham system

Re-derives the Runge-Gross theorem for QED

Abstract

We prove a generalization of the van Leeuwen theorem towards quantum electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham construction for coupled quantized matter and electromagnetic fields. Thereby we circumvent the symmetry-causality problems associated with the action-functional approach to Kohn-Sham systems. We show that the effective external four-potential and four-current of the Kohn-Sham system are uniquely defined and that the effective four-current takes a very simple form. Further we rederive the Runge-Gross theorem for quantum electrodynamics.