A Green-function unification of weak interactions with environmental dressing

Abstract

Weak, non-covalent interactions such as electrostatics, induction, and dispersion are commonly treated as distinct physical mechanisms, often using separate models and approximations. Here, we present a unified quantum-electrodynamical framework in which all weak interactions between neutral or charged subsystems emerge from a single interaction Hamiltonian and are expressed entirely in terms of electromagnetic Green functions. Starting from macroscopic QED in arbitrary linear environments, we derive compact master formulas that generate permanent electrostatic, mixed induction, and fully induced (dispersion) interactions on equal footing. Monopoles, dipoles, and quadrupoles are treated consistently within the same multipole expansion, leading to a common structural form in which all interaction channels are obtained from contractions of multipole moments and response functions with Green tensors. Environmental effects enter universally through dressed Green functions. The standard non-retarded free-space limits, including Keesom, Debye, and London/van der Waals interactions, are recovered as a consistency check of the formalism. Beyond this validation, the formulation shows that once the general expressions are established, different physical scenarios, such as interfaces, confinement, or polarisable continua, can be treated by direct substitution of the corresponding Green function, without reformulating the interaction for each case. This elevates Green functions to a universal organising principle for weak interactions in complex environments.