Dispersion forces on Proca electrodynamics

Abstract

The effects of a finite photon mass have been analyzed in multiple scenarios involving dispersive forces. To describe the interactions relevant to such forces, Proca electrodynamics was employed. Initially, we considered the dispersion interaction between two atoms in their ground states, for which we determined the interaction potential over all distance regimes. As in the case mediated by massless photons, we also determined the dispersive potential in two asymptotic regimes: the non-retarded regime and the retarded (here referred to as asymptotic) regime. We also concluded that the photon mass, by introducing a new length scale, modifies the conditions required for the validity of each regime. For instance, for a given interatomic separation, the larger the photon mass, the more accurate the non-retarded approximation becomes. The effects of non-additivity in dispersive forces were also considered within Proca electrodynamics. These effects were divided into two main groups: free atoms interacting with each other, and atoms interacting with grounded, neutral, conducting surfaces. For the first group, we found that the photon mass always weakens the non-additive interaction and reduces its relevance compared to the total dispersive interaction. For the interaction between atoms and surfaces, however, we found that there are scenarios in which the non-additive force becomes dominant for nonzero photon mass values.