Virial Relations for Electrons Coupled to Quantum Field Modes

[Image: see text] In this work, we present a set of virial relations for many electron systems coupled to both classical and quantum fields, described by the Pauli–Fierz Hamiltonian in dipole approximation and using length gauge. Currently, there is growing interest in solutions of this Hamiltonian because of 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.