Here {|Ψ a (R)⟩} are the polaritonic state at R which can be written in expressed in the adiabatic-Fock state representation as |Ψ a (R)⟩ = α,n C a α,n |ψ α (R ξ )⟩, n⟩ and are obtained by diagonalizing Ĥpl (see Eqn. 111). Within this representation, the total light-matter Hamiltonian is written as