Tokatly and Maitra independently introduced already some years ago the photon degrees of freedom in the exactfactorization formalism for applications of quantum electrodynamics in the context of molecular polaritons. The field of polaritonic chemistry started to emerge little over a decade ago as a way to affect (photo)chemical reactions by creating hybrid light-matter states, i.e., the polaritons, when the strong-coupling regime between the molecular excitations and confined light is achieved in optical and plasmonic cavities . In chemical physics and physical chemistry, we have witnessed a large variety of ideas aiming to reformulate in cavities concepts such as the Born-Oppenheimer approximation , nonadiabatic dynamics , density functional theory and other electronic-structure theories , and the exact factorization . In this respect, Maitra followed up on her preliminary work with various analysis of the dynamics of electronic and of electron-nuclear systems in optical microcavities in the regime of strong light-matter coupling. In particular, these works drew the connection between the exact factorization and the "usual" polaritonic picture as well as introduced the idea of trajectories to approximate either the nuclear or the photonic dynamics .