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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 is very much already due to Maxwell himself (following Thomson). The elimination of 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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