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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.
Invariance of the form of an equation under an arbitrary coordinate transformation is customarily referred to as general covariance, and equations with this property are referred to as written in the covariant form. General covariance is a special case of gauge invariance.
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.
Gauge theory gravity (GTG) is a theory of gravitation cast in the mathematical language of geometric algebra. To those familiar with general relativity , it is highly reminiscent of the tetrad formalism although there are significant conceptual differences.
A more modern interpretation of the physical content of the original principle of general covariance is that the Lie group GL 4 (R) is a fundamental "external" symmetry of the world. Other symmetries, including "internal" symmetries based on compact groups , now play a major role in fundamental physical theories.
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 ...
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 ...
This was the first clear statement of the principle of gauge invariance in physical law. Einstein believed that the hole argument implies that the only meaningful definition of location and time is through matter. A point in spacetime is meaningless in itself, because the label which one gives to such a point is undetermined.