Historical Roots of Gauge Invariance
J. D. Jackson
University of California, Berkeley
Lawrence Berkeley National Laboratory

A number of reviews of gauge theories cover the period from about 1929 (Weyl's major paper on the subject) to the present day, with stress on the post-Yang-Mills epoch. Lev Okun and I address the "pre-history" of the subject, starting with Ampere, Neumann, Weber, and others, and the debates over the "correct" form of the vector potential. The story continues with Maxwell, Lorenz, Helmholtz, Clausius, and Lorentz by which time the idea of different, equivalent gauges for the potentials in classical electromagnetism had been clarified completely. We then discuss the annus mirabilus, 1926, with Fock's discovery of the phase transformation of the wave function that must accompany a gauge change of the potentials. The unfair belittlement of the contributions of Lorenz and Fock are aired. Portraits of all the "electricians" are presented as the story unfolds.

[J. D. Jackson and Lev Okun, Rev, Mod.Phys. Vol. 73, 663- 680 (2001)]