## 1 Introduction  
Fundamental theoretical studies of resonance energy transfer (RET) [1], especially those involving the use of quantum electrodynamics (QED) theory [2; 3; 4; 5; 6; 7], have largely concentrated on the exchange of energy taking place between two interacting particles, a donor, \(D\), and an acceptor, \(A\). These species may be atoms, molecules, chromophores, functional groups, or other such material entities that engage with electromagnetic radiation and undergo electronic and/or vibrational excitation and de-excitation to and from quantized energy levels. Migration of energy occurs from the initially excited \(D\), to \(A\), which is initially in its ground state, with \(A\) capturing all of the excitation energy in a resonant process. According to QED, energy is conveyed from emitter to absorber at the speed of light through the propagation of a single virtual photon. This is because coupling between matter at the microscopic scale of atoms and molecules is due to electromagnetic forces, which are mediated by gauge bosons. These are the light quanta, a direct manifestation of quantization of the electromagnetic field, which is a key feature of QED. Perturbation theory has been used to evaluate the Fermi golden rule transfer rate as a function of the pair separation distance, \(R\), for oriented and freely tumbling particles [8; 9; 10; 11; 12; 13; 14; 15; 16]. From these results, it has been established that at short inter-nuclear distances, the exchange of energy is radiationless, exhibiting an \(R^{-6}\) Forster-type dependence, while in the other extreme, corresponding to the far-zone, the rate has inverse square behavior, illustrative of a radiative transfer mechanism. While a majority of works have understandably focused on RET in free space, considerable effort has also been devoted to exploring the effects of a medium in modifyingthe rate [17,18] as environment-influenced energy transfer is the usual situation commonly found in diverse scientific fields and technological applications. An early method to account for the dispersive and dissipative properties of a bath, and a means to introduce the refractive index, was to view the medium as possessing a uniform dielectric constant, with connection to the bulk polarizability made via the Clausius-Mossotti relation [19]. More rigorous treatments have followed. These have included quantizing both the electromagnetic field and a dielectric medium, with the latter viewed as a collection of identical atoms arranged as a lattice, within which a chromophore or a pair of interacting particles is embedded [20, 21, 22, 23, 24]. The elementary bosonic excitations of the bath are now medium-dressed photons or polaritons, allowing for individual emission and absorption events to occur. One such particle is exchanged in RET taking place in a surrounding environment, altering the rate relative to its vacuum value through the appearance of a complex refractive index, local field and screening factors, and the correct diminution of the amplitude via exponential decay. This approach has been extended within the framework of macroscopic QED in which the medium is taken to be a linear magnetodielectric [25]. It has recently been applied to compute RET, for instance, in treating coupling to plasmons in nanostructure systems [26, 27, 28]. Instead of viewing the direct transfer between \(D\) and \(A\) taking place in an environment, an alternative approach is to picture exchange mediated by microscopic particles, and to consider how constructing a microscopic many-body theory modifies the rate. The extrapolation of the results obtained for the few-body case to an infinite number of mediators allows a comparison to be made with macroscopic treatments. A few calculations have been performed of the rate mediated by a neutral, polarizable third molecule that either serves as a bridging species, relaying energy between \(D\) and \(A\), or is coupled only to \(D\) or only to \(A\)[29, 30, 31, 32, 33], including interference terms between direct and various indirect pathways.