Non-local effects in classical electrodynamics: external sources and material boundary

In this paper, we explore non-local effects in electrodynamics in the presence of external sources and a material boundary. Specifically, we consider a model where Maxwell’s electrodynamics is modified by a specific non-local term, which describes the phenomenological Cornell’s confining potential. First, we study the interaction between stationary field sources, describing point-like charges, Dirac strings, and point-like dipoles. In this analysis, we demonstrate that the ground state energy of the hydrogen atom and also the dipole-dipole interaction are modified by these non-local effects, which contributions are used to set a stringent bounds upon the model’s parameter (measuring the non-locality effects). Moreover, we show that the non-locality stems an interaction between Dirac strings, which is absent in the Maxwell theory. In a complementary study, we investigate this model in the presence of a conducting plate. In this case, we calculate the propagator for the gauge field and the interaction force between the conducting plate and a point-like charge. It is shown that the image method is not valid for this non-local theory.