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A gauge theory is a type of theory in physics. The word gauge means a measurement, a thickness, an in-between distance (as in railroad tracks), or a resulting number of units per certain parameter (a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition). [1]
The concept and the name of gauge theory derives from the work of Hermann Weyl in 1918. [1] Weyl, in an attempt to generalize the geometrical ideas of general relativity to include electromagnetism, conjectured that Eichinvarianz or invariance under the change of scale (or "gauge") might also be a local symmetry of general relativity.
This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.
Seiberg–Witten theory; Six-dimensional holomorphic Chern–Simons theory; Slavnov–Taylor identities; Soft photon; Stable Yang–Mills connection; Stable Yang–Mills–Higgs pair; Stueckelberg action; Supersymmetric gauge theory; Synthetic gauge field
Gauge symmetry is an example of a local symmetry, with the symmetry described by a Lie group (which mathematically describe continuous symmetries), which in the context of gauge theory is called the gauge group of the theory. Quantum chromodynamics and quantum electrodynamics are famous examples of gauge theories.
A gauge theory of elementary particles is a very attractive potential framework for constructing the Grand Unified Theory of physics. Such a theory has the very desirable property of being potentially renormalizable—shorthand for saying that all calculational infinities encountered can be consistently absorbed into a few parameters of the theory.
The gauge covariant derivative is used in many areas of physics, including quantum field theory and fluid dynamics and in a very special way general relativity. If a physical theory is independent of the choice of local frames, the group of local frame changes, the gauge transformations , act on the fields in the theory while leaving unchanged ...
There are several distinct frameworks within which higher gauge theories have been developed. Alvarez et al. [1] extend the notion of integrability to higher dimensions in the context of geometric field theories. Several works [2] of John Baez, Urs Schreiber and coauthors have developed higher gauge theories heavily based on category theory.