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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.
Generally, any theory that has the property of gauge invariance is considered a gauge theory. For example, in electromagnetism the electric field E and the magnetic field B are observable, while the potentials V ("voltage") and A (the vector potential ) are not. [ 4 ]
In gauge theory, which studies a particular class of fields which are of importance in quantum field theory, different fields are used in Lagrangians that are invariant under local gauge transformations. Kinetic terms involve derivatives of the fields which by the above arguments need to involve gauge covariant derivatives.
Gauge theory in mathematics should not be confused with the closely related concept of a gauge theory in physics, which is a field theory that admits gauge symmetry. In mathematics theory means a mathematical theory , encapsulating the general study of a collection of concepts or phenomena, whereas in the physical sense a gauge theory is a ...
A quantity or expression that does not depend on the gauge function is said to be gauge invariant: All physical observables are required to be gauge invariant. A gauge transformation from the Coulomb gauge to another gauge is made by taking the gauge function to be the sum of a specific function which will give the desired gauge transformation ...
In quantum field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops.They encode all gauge information of the theory, allowing for the construction of loop representations which fully describe gauge theories in terms of these loops.
The aim of the loop representation in the context of Yang–Mills theories is to avoid the redundancy introduced by Gauss gauge symmetries allowing to work directly in the space of physical states (Gauss gauge invariant states). The idea is well known in the context of lattice Yang–Mills theory (see lattice gauge theory). Attempts to explore ...
The motivation for a supersymmetric version of gauge theory can be the fact that gauge invariance is consistent with supersymmetry. The first examples were discovered by Bruno Zumino and Sergio Ferrara, and independently by Abdus Salam and James Strathdee in 1974.