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A non-local action functional for electrodynamics depending on the electricand magnetic fields, instead of potentials, has been proposed in theliterature. In this work we elaborate and improve this proposal. We also usethis formalism to confront the electric-magnetic duality symmetry of theelectromagnetic field and the Aharonov--Bohm effect, two subtle aspects ofelectrodynamics that we examine in a novel way. We show how the former can bederived from the simple harmonic oscillator character of vacuumelectrodynamics, while also demonstrating how the magnetic version of thelatter naturally arises in an explicitly non-local manner.

A Non-Local Action for Electrodynamics: Duality Symmetry and the Aharonov-Bohm Effect, Revisited