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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.
Later Hermann Weyl, inspired by success in Einstein's general relativity, conjectured (incorrectly, as it turned out) in 1919 that invariance under the change of scale or "gauge" (a term inspired by the various track gauges of railroads) might also be a local symmetry of electromagnetism.
The direct analogue of the "gauge freedom" of the gauge covariant derivative is the arbitrariness of the choice of an orthonormal d-Bein at each point in space-time: local Lorentz invariance [citation needed]. However, in this case the more general independence of the choice of coordinates for the definition of the Levi Civita connection gives ...
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 ...
In contrast to the Berry connection, which is physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions in the parameter space, and has proven to be an essential physical ingredient for understanding a variety of electronic properties. [4] [5]
The ability to vary the gauge potential at different points in space and time (by changing (,)) without changing the physics is called a local invariance. Electromagnetic theory possess the simplest kind of local gauge symmetry called () (see unitary group). A theory that displays local gauge invariance is called a gauge theory.
If we were using one gauge for all fields, X X would be gauge invariant. However, we need to convert gauge I to gauge II, transforming X to (e −V) q X. So, the gauge invariant quantity is X e −qV X. In gauge I, we still have the residual gauge e Λ where ¯ ˙ = and in gauge II, we have the residual gauge e Λ satisfying d α Λ = 0. Under ...
The line is the equivalent of a gauge function; it need not be straight. Almost any line is a valid gauge fixing, i.e., there is a large gauge freedom. In summary, to tell whether the rod is twisted, the gauge must be known. Physical quantities, such as the energy of the torsion, do not depend on the gauge, i.e., they are gauge invariant.