  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.
