where ξ M βα (r) ≡ ρ M 0j (r, r) = ψ α (r)ψ * β (r). Recall that we have explicitly removed the photonic transition density from appearing, but, in principle, could also appear to give a more general expression. The generalization of Eq. 13 to include all possible one-particle matter, photonic, and mixed matter-photonic observables is shown in Eq. 6.