Canonical HF theory attempts to describe a many-body system's ground state by the use of a single Slater determinant, |Φ HF ⟩, that yields an uncorrelated ground state. This is usually the basis for so-called post-HF methods that will be discussed later, such as the configuration interaction (CI) and coupled cluster (CC) methods. For the polaritonic system, one extends this ideology to include the photonic DOFs such that the uncorrelated electrons and photons use the following direct product state. However, to simplify the problem, many authors have opted to use the coherent state basis 148 for their implementations of the scQED schemes 100,157 for the photonic DOFs, which alleviates some of the complexity in notation as well as provides a useful interpretation of the effects of the cavity on the ground state properties.