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