where we have explicitly used the orthonormality relation of the Fock states ⟨n|m⟩ = δ nm . This expression implies that the ρM 0j mixes all molecular transition densities according to the expansion coefficients of the polaritonic states. One can perform an integration over all but one of the electronic DOFs, arriving at the matter-projected oneparticle transition density matrix ρ M 0j (r e , r h ) as fol-lows,