  Gauge invariance is the basis of the modern theory of electroweak and strong
interactions (the so called Standard Model). The roots of gauge invariance go
back to the year 1820 when electromagnetism was discovered and the first
electrodynamic theory was proposed. Subsequent developments led to the
discovery that different forms of the vector potential result in the same
observable forces. The partial arbitrariness of the vector potential A brought
forth various restrictions on it. div A = 0 was proposed by J. C. Maxwell;
4-div A = 0 was proposed L. V. Lorenz in the middle of 1860's . In most of the
modern texts the latter condition is attributed to H. A. Lorentz, who half a
century later was one of the key figures in the final formulation of classical
electrodynamics. In 1926 a relativistic quantum-mechanical equation for charged
spinless particles was formulated by E. Schrodinger, O. Klein, and V. Fock. The
latter discovered that this equation is invariant with respect to
multiplication of the wave function by a phase factor exp(ieX/hc) with the
accompanying additions to the scalar potential of -dX/cdt and to the vector
potential of grad X. 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 non-abelian gauge theories started in 1954 with the
paper by C. N. Yang and R. L. Mills.
