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Gauge theories refer to a general class of quantum field theories, used for the description of subatomic particles and their interactions.
James Clerk Maxwell
David Hilbert
Herman Weyl
The earliest field theory to have gauge symmetry was Maxwell's formulation of electrodynamics from 1864 and 65. His paper was titled, "A Dynamical Theory of the Electromagnetic Field."
David Hilbert, had derived the Einstein field equations, by postulating the invariance of the action under a general coordinate transformation.
Herman Weyl, in an attempt to unify general relativity with electromagnetism, proposed the "Eichinvarianz." This was an invariance under changes in scale. He conjectured that this also could be a symmetry of general relativity.
After the development of quantum mechanics, Weyl, Vladimir Flock and Fritz London, modified gauge by replacing the scale factor with a complex quantity. They turned the scale transformation into a change of phase. This is a U(1) gauge symmetry and was popularized by Wolfgang Pauli in 1941.
C. N. Yang
Robert Mills
In 1954, C. N. Yang and Robert Mills, attempting to resolve a great confusion in particle physics, introduce non-abelian gauge theories as models to understand the strong nuclear interaction, which works to hold the nucleus of the atoms together.
Their ideas later found applications in quantum field theory for the weak nuclear force and its unification with electromagnetism, the electroweak interaction.
The Standard Model unifies the description of electromagnetism, the strong and weak nuclear forces in the language of gauge theory.
The importance of gauge theories is apparent in the success of quantum field theory's unified description of electromagnetism, and the strong and weak nuclear forces.
The Standard Model is a gauge theory with the group SU(3) x SU(2) x U(1).
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