Historical roots of gauge invariance

By J. Jackson, L. Okun. 2000

310 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

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Citations in the corpus

The mass of the photon (2004, background): “…and Toms 1985, Lehnert and Roy 1998, Lehnert 2000), B(3) field theory (Evans and Vigier 1994, Evans and Crowell 2001), new weak force predictions, and others (Bartlett and Lögl 1988, Cameron et al 1993, Krause et al 1994, Kloor et al 1994, Jackson and Okun 2001, Prokopec et al 2002, Kohler 2002).”
General Relativity and Cosmology: Unsolved Questions and Future Directions (2016, background): “ity r at a particular point in space x relative to the mean r at some time parameterised by the scale factor a, and can be expressed as a dimensionless density contrast: d(x, a) = r(x, a) r(a) r(a) . (95) Universe 2016, 2, 23 38 of 82 This quantity can be understood as the dimensionless density pert”
Photon and graviton mass limits (2008, background): “8 See the reviews of Jackson and Okun (20) and of Wu and Yang”
An introduction to spontaneous symmetry breaking (2019, background): “eit. In fact, the term \gauge invariance" was coined by Hermann Weyl in 1919 in German as eichinvarianz, where eich (gauge) refers to the scale or standard dimension used by a measurement device [10]. It is the ‘choice of tick marks’, and we are free to choose the ticks on our measurement devic”