Historical roots of gauge invariance

Gauge invariance is the basis of the modern theory of electroweak and stron g interactions (the so-called standard model). A number of authors have dis cussed 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 elec tromagnetism was discovered and the first electrodynamic theory was propose d. We describe the 19th century developments that led to the discovery that different forms of the vector potential (differing by the gradient of a sc alar function) are physically equivalent, if accompanied by a change in the scalar potential: A -->A'=A+del chi, Phi --> Phi'=Phi-partial derivative c hi /c partial derivativet. L. V. Lorenz proposed the condition partial deri vative (mu)A(mu)=0 in the mid-1860s, but this constraint is generally misat tributed to the better known H. A. Lorentz. In the work in 1926 on the rela tivistic wave equation for a charged spinless particle in an electromagneti c field by Schrodinger, Klein, and Fock, it was Fock who discovered the inv ariance of the equation under the above changes in A and Phi if the wave fu nction was transformed according to psi --> psi=psi exp(ie chi /hc). In 192 9, H. Weyl proclaimed this invariance as a general principle and called it Eichinvarianz in German and gauge invariance in English. The present era of non-Abelian gauge theories started in 1954 with the paper by Yang and Mill s on isospin gauge invariance.