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added these pointers:
A. C. T. Wu, Chen Ning Yang, Evolution of the concept of vector potential in the description of the fundamental interactions, International Journal of Modern Physics A 21 16 (2006) 3235-3277 [doi:10.1142/S0217751X06033143]
Chen Ning Yang, The conceptual origins of Maxwell’s equations and gauge theory, Phyics Today 67 11 (2014) [doi:10.1063/PT.3.2585, pdf]
Reading through these, I realize that I had not actually appreciated before that the introduction of the EM-potential $A$ is very much already due to Maxwell himself (following Thomson). The elimination of $A$ from the original equations to yield those that now bear Maxwell’s name is apparently (p. 6) due to Heaviside and Hertz, about 30 years later.
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