On Feynman's handwritten notes on electromagnetism and the idea of introducing potentials before fields

Abstract

In his recently discovered handwritten notes on "An alternate way to handle electrodynamics" dated on 1963, Richard P. Feynman speculated with the idea of getting the inhomogeneous Maxwell's equations for the electric and magnetic fields from the wave equation for the vector potential. With the aim of implementing this pedagogically interesting idea, we develop in this paper the approach of introducing the scalar and vector potentials before the electric and magnetic fields. We consider the charge conservation expressed through the continuity equation as a basic axiom and make a heuristic handle of this equation to obtain the retarded scalar and vector potentials, whose wave equations yield the homogeneous and inhomogeneous Maxwell's equations. We also show how this axiomatic-heuristic procedure to obtain Maxwell's equations can be formulated covariantly in the Minkowski spacetime.

arXiv commentThe paper includes an extract of Feynman's first handwritten note on his "Alternate Way to Handle Electrodynamics."

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Cited by in corpus (3)

• Electromagnetic potentials in curved spacetimes
• Derivation and physical interpretation of the general solutions to the wave equations for electromagnetic potentials
• On the connection between Lenz's law and relativity