Any polaritonic observable Ô can be described with any basis of light and matter, e.g. adiabatic-Fock (Section 3.1.1), PFS (Section 3.1.2), or any other. Note that this is a more general case than was done in Eq. 21. Here, we will choose the adiabatic-Fock basis for conceptual simplicity, but all of the main points are easily transferable to another basis by unitary transformation. The matrix elements of the polaritonic observable Ô can be expanded in the adiabatic-Fock basis (Eq. 20) as,