  We provide theory and formal insight on the Green function quantization
method for absorptive and dispersive spatial-inhomogeneous media in the context
of dielectric media. We show that a fundamental Green function identity, which
appears, e.g., in the fundamental commutation relation of the electromagnetic
fields, is also valid in the limit of non-absorbing media. We also demonstrate
how the zero-point field fluctuations yields a non-vanishing surface term in
configurations without absorption, when using a more formal procedure of the
Green function quantization method. We then apply the presented method to a
recently developed theory of photon quantization using quasinormal modes
[Franke et al., Phys. Rev. Lett. 122, 213901 (2019)] for finite nanostructures
embedded in a lossless background medium. We discuss the strict dielectric
limit of the commutation relations of the quasinormal mode operators and
present different methods to obtain them, connected to the radiative loss for
non-absorptive but open resonators. We show exemplary calculations of a fully
three-dimensional photonic crystal beam cavity, including the lossless limit,
which supports a single quasinormal mode and discuss the limits of the
commutation relation for vanishing damping (no material loss and no radiative
loss).
