Often, for finite molecular systems, the Pauli-Fierz (PF) Hamiltonian ĤPF is chosen to model the interactions between the molecular and photonic degrees of freedom inside an optical or plasmonic cavity. We will first introduce the single-mode, single-molecular description; although, later in Section 2.3, we will generalize to the collective manymode, many-molecule Hamiltonian needed to describe experimental conditions. At this level, the PF Hamiltonian can be written as,