  Cavity quantum electrodynamics (CQED) and its extensions are widely used for
the description of exciton-polariton systems. However, the exciton-polariton
models based on CQED vary greatly within different contexts. One of the most
significant discrepancies among these CQED models is whether one should include
direct intermolecular interactions in the CQED Hamiltonian. To answer this
question, in this article, we derive an effective dissipative CQED model
including free-space dipole-dipole interactions (CQED-DDI) from a microscopic
Hamiltonian based on macroscopic quantum electrodynamics. Dissipative CQED-DDI
successfully captures the nature of vacuum fluctuations in dielectric media and
separates it into the free-space effects and the dielectric-induced effects.
The former include spontaneous emissions, dephasings and dipole-dipole
interactions in free space; the latter include exciton-polariton interactions
and photonic losses due to dielectric media. We apply dissipative CQED-DDI to
investigate the exciton-polariton dynamics (the population dynamics of
molecules above a plasmonic surface) and compare the results with those based
on the methods proposed by several previous studies. We find that direct
intermolecular interactions are a crucial element when employing CQED-like
models to study exciton-polariton systems involving multiple molecules.
