  Over the last two decades, the hierarchical equations of motion (HEOM) of
Tanimura and Kubo have become the equation of motion-based tool for numerically
exact calculations of system-bath problems. The HEOM is today generalized to
many cases of dissipation and transfer processes through an external bath. In
spatially extended photonic systems, the propagation of photons through the
bath leads to retardation/delays in the coupling of quantum emitters. Here, the
idea behind the HEOM derivation is generalized to the case of photon
retardation and applied to the simple example of two dielectric slabs. The
derived equations provide a simple reliable framework for describing
retardation and may provide an alternative to path integral treatments.
