where the photonic DOFs have been traced out, leaving only the electronic contributions. Here, ξ M αβ (r) = ψ * β (r)ψ α (r) is the αβ th electronic transition density in real space r and ρ0j = |Φ j ⟩ ⟨Φ 0 | is the 0j th polaritonic density operator. More details on calculating observables can be found in Sec. 3.1.3. The light-matter hybridization leads to superpositions between photon-dressed electronic states, which leads to various electronic transition densities mixing through the polaritonic expansion coefficients in the adiabatic-Fock basis (see Eq. 20). The matter-projected polaritonic transition density 39;37 is only one of many ways to examine the character of the molecular part of the polaritonic excitation.