Virial relations for electrons coupled to quantum field modes

TL;DR

This paper derives virial relations for many-electron systems interacting with quantum field modes, aiding in understanding their energy properties and connections to mass renormalization within quantum electrodynamics.

Contribution

It introduces a set of virial relations for the Pauli--Fierz Hamiltonian in the dipole approximation, linking energy calculations to potential functions in QED density functional theory.

Findings

Virial relations connect total energy and potentials in coupled electron-field systems.

Demonstrates the relevance of virial relations for mass renormalization.

Provides an exact method to compute energies in cavity QED systems.

Abstract

In this work we present a set of virial relations for many electron systems coupled to field modes, described by the Pauli--Fierz Hamiltonian in dipole approximation and using length gauge. Currently, there is growing interest in solutions of this Hamiltonian due to its relevance for describing molecular systems strongly coupled to photonic modes in cavities, and in the possible modification of chemical properties of such systems compared to the ones in free space. The relevance of such virial relations is demonstrated by showing a connection to mass renormalization and by providing an exact way to obtain total energies from potentials in the framework of Quantum Electrodynamical Density Functional Theory.