Historical roots of gauge invariance
Abstract
Gauge invariance is the basis of the modern theory of electroweak and strong interactions (the socalled standard model). A number of authors have discussed the ideas and history of quantum guage theories, beginning with the 1920s, but the roots of gauge invariance go back to the year 1820 when electromagnetism was discovered and the first electrodynamic theory was proposed. We describe the 19th century developments that led to the discovery that different forms of the vector potential (differing by the gradient of a scalar function) are physically equivalent, if accompanied by a change in the scalar potential: A>A'=A+∇χ, Φ>Φ'=Φ ∂χ/c∂t. L. V. Lorenz proposed the condition ∂_{μ}A^{μ}=0 in the mid1860s, but this constraint is generally misattributed to the better known H. A. Lorentz. In the work in 1926 on the relativistic wave equation for a charged spinless particle in an electromagnetic field by Schrödinger, Klein, and Fock, it was Fock who discovered the invariance of the equation under the above changes in A and Φ if the wave function was transformed according to ψ>ψ'=ψ exp(ieχ/ħc). In 1929, H. Weyl proclaimed this invariance as a general principle and called it Eichinvarianz in German and gauge invariance in English. The present era of nonAbelian gauge theories started in 1954 with the paper by Yang and Mills on isospin gauge invariance.
 Publication:

Reviews of Modern Physics
 Pub Date:
 July 2001
 DOI:
 10.1103/RevModPhys.73.663
 arXiv:
 arXiv:hepph/0012061
 Bibcode:
 2001RvMP...73..663J
 Keywords:

 01.65.+g;
 11.15.q;
 03.50.De;
 11.30.Er;
 History of science;
 Gauge field theories;
 Classical electromagnetism Maxwell equations;
 Charge conjugation parity time reversal and other discrete symmetries;
 High Energy Physics  Phenomenology;
 Physics  Physics Education;
 Physics  History of Physics
 EPrint:
 finalfinal, 34 pages, 1 figure, 106 references (one added with footnote since v.2)