Constraints for electric charge from Maxwell’s equations and boundary conditions

Abstract

Abstract Certain boundary conditions constrain the forms that the electromagnetic field can take in a theory, in particular the boundary conditions inherent to closed spaces. According to Maxwell’s equations, this can give rise to constraints for the electric charge in the theory. We identify three such ‘boundary constraints’ for electric charge and highlight some of their myriad implications, touching upon a wealth of topics including the self-consistency of practical calculations, the nature of dark matter, the origin of electric-charge quantisation and the shape of the Universe. Furthermore, we explain that magnetic analogues of our boundary constraints offer new insights into the possible existence of magnetic monopoles and dyons.