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.
Highlights
Electric charge is a fundamental quantity in physics, yet there is much still to be understood
The basic theory of classical electrodynamics [1] allows us to choose the electric charges of particles independently with any values in the continuous interval (− ∞, ∞ )C
We identify three ‘boundary constraints’ for electric charge, so named because they derive from Maxwell’s equations and the boundary conditions in relevant theories: 1. The zero-point electric charge must vanish
Summary
Constraints for electric charge from Maxwell’s equations and boundary conditions. Certain boundary conditions constrain the forms that the electromagnetic field can take in a theory, in licence. Any further distribution of this work must maintain can give rise to constraints for the electric charge in the theory. We identify three such ‘boundary attribution to the constraints’ for electric charge and highlight some of their myriad implications, touching upon a author(s) and the title of the work, journal citation wealth of topics including the self-consistency of practical calculations, the nature of dark matter, the and DOI. Origin of electric-charge quantisation and the shape of the Universe. We explain that magnetic analogues of our boundary constraints offer new insights into the possible existence of magnetic monopoles and dyons
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