  When light and matter interact strongly, the coupled system inherits
properties from both constituents. It is consequently possible to alter the
properties of either by engineering the other. This intriguing possibility has
lead to the emergence of the cavity-materials-engineering paradigm which seeks
to tailor material properties by engineering the fluctuations of a dark
electromagnetic environment. The theoretical description of hybrid light-matter
systems is complicated by the combined complexity of a realistic description of
the extended electronic and quantum electromagnetic fields. Here we derive an
effective, non-perturbative theory for low dimensional crystals embedded in a
paradigmatic Fabry-P\'erot resonator in the long-wavelength limit. The theory
encodes the multi-mode nature of the electromagnetic field into an effective
single-mode scheme and it naturally follows from requiring a negligible
momentum transfer from the photonic system to the matter. Crucially, in the
effective theory the single light mode is characterized by a finite effective
mode volume even in the limit of bulk cavity-matter systems and can be directly
determined by realistic cavity parameters. As a consequence, the coupling of
the effective mode to matter remains finite for bulk materials. By leveraging
on the realistic description of the cavity system we make our effective theory
free from the double counting of the coupling of matter to the electromagnetic
vacuum fluctuations of free space. Our results provide a substantial step
towards the realistic description of interacting cavity-matter systems at the
level of the fundamental Hamiltonian, by effectively including the
electromagnetic environment and going beyond the perfect mirrors approximation.
