A classical field theory is a gauge theory when its description has a local redundancy represented by gauge transformations. A gauge field defines the covariant derivative that compares matter fields at different points, and its gauge field strength measures the curvature of that comparison. Electromagnetism is the familiar Abelian example; Yang-Mills theory generalizes it to a non-Abelian internal group. Both classical equations and their quantum field theory can have this structure. Physically equivalent gauge descriptions must give the same observables, even though the gauge potential changes.
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Gauge theory is a type of field theory in which the Lagrangian (the mathematical function that describes the dynamics of the system) is invariant under certain local transformations, or "gauge transformations." These transformations can vary from point to point in spacetime and are foundational to our understanding of fundamental forces in physics, particularly in the framework of particle physics and the Standard Model. ### Key Concepts 1.
The term and idea was first introduced initialized by Hermann Weyl when he was working on combining electromagnetism and general relativity to formulate Maxwell's equations in curved spacetime in 1918 and published as Gravity and electricity by Hermann Weyl (1918). Based on perception that symmetry implies charge conservation. The same idea was later adapted for quantum electrodynamics, a context in which is has even more impact.