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A fully relativistically covariant and manifestly gauge invariant formulationof classical Maxwell electrodynamics is presented, purely in terms of gaugeinvariant potentials without entailing any gauge fixing. We show that theinhomogeneous equations satisfied by the physical scalar and vector potentials(originally discovered by Maxwell) have the same symmetry as the isometry ofMinkowski spacetime, thereby reproducing Einstein's incipient approach leadingto his discovery of special relativity as a spacetime symmetry. To arrive atthis conclusion, we show how the Maxwell equations for the potentials followfrom stationary electromagnetism by replacing the Laplacian operator by thed'Alembertian operator, while making all variables dependent on space and time.We also establish consistency of these equations by deriving them from thestandard Maxwell equations for the field strengths, showing that there is aunique projection operator which projects onto the physical potentials.Properties of the physical potentials are elaborated through their iterativeN\"other coupling to a charged scalar field leading to the Abelian Higgs model,and through a sketch of the Aharonov-Bohm effect, where dependence of theAharonov-Bohm phase on the physical vector potential is highlighted.

Maxwell Electrodynamics in terms of Physical Potentials