Conserving approximations in cavity quantum electrodynamics: Implications for density functional theory of electron-photon systems

TL;DR

This paper derives an exact momentum balance equation for electrons in cavity QED, discusses its implications for density functional theory, and shows that certain approximations can be made conserving and accurate.

Contribution

It introduces a generalized concept of erivability for constructing conserving approximations in QED-TDDFT, ensuring correct momentum balance.

Findings

The exact momentum/force balance equation for cavity QED is derived.

A conserving approximation for QED-TDDFT is identified and validated.

Implications for improving electron-photon density functional methods are discussed.

Abstract

By analyzing the many-body problem for non-relativistic electrons strongly coupled to photon modes of a microcavity I derive the exact momentum/force balance equation for cavity quantum electrodynamics. Implications of this equation for the electron self-energy and the exchange-correlation potential of quantum electrodynamic time-dependent density functional (QED-TDDFT) are discussed. In particular I generalize the concept of $\Phi$-derivability to construct approximations which ensure the correct momentum balance. It is shown that a recently proposed optimized effective potential approximation for QED-TDDFT is conserving and its possible improvements are discussed.