Maxwell Electrodynamics in Terms of Physical Potentials
Abstract
A fully relativistically covariant and manifestly gauge invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) have the same symmetry as the isometry of Minkowski spacetime, thereby reproducing Einstein's incipient approach leading to his discovery of special relativity as a spacetime symmetry. To arrive at this conclusion, we show how the Maxwell equations for the potentials follow from stationary electromagnetism by replacing the Laplacian operator by the d'Alembertian operator, while making all variables dependent on space and time. We also establish consistency of these equations by deriving them from the standard Maxwell equations for the field strengths, showing that there is a unique projection operator which projects onto the physical potentials. Properties of the physical potentials are elaborated through their iterative Nöther coupling to a charged scalar field leading to the Abelian Higgs model, and through a sketch of the AharonovBohm effect, where dependence of the AharonovBohm phase on the physical vector potential is highlighted.
 Publication:

Symmetry
 Pub Date:
 July 2019
 DOI:
 10.3390/sym11070915
 arXiv:
 arXiv:1905.13748
 Bibcode:
 2019Symm...11..915M
 Keywords:

 Physics  General Physics
 EPrint:
 9 pages Latex2e. arXiv admin note: contains material formerly in arXiv:1801.07603