reactivity in a general way by tuning the fundamental properties of photons and provides a new paradigm for enabling chemical transformations that can profoundly impact catalysis, energy production, and the field of chemistry at large. However, recent experimental demonstrations of this modification of chemical reactivity are not well understood and, in some cases, not reproducible . Since these polaritonic systems often require a quantum mechanical description of the photonic modes, existing physical chemistry theories for chemical reactions are no longer directly applicable to these hybrid systems, requiring a more exact QED approach. While the fundamental theories of QED has been known for decades, directly translating this knowledge to explain measurements of polariton chemistry remains as a major challenge in both theoretical chemistry and quantum optics. Namely, the mechanism behind the strong coupling of a mesoscopic ensemble of molecules to a single optical cavity is still not fully understood. The basic theory for describing the modes in different types of cavity is also briefly discussed in Sec. 2 and 5.3.