Gauge theory is a conversion from one such force field into another version of the force field. In terms of fields such as electromagnetic force, gravitational force and force between elementary particles, i.e. weak force and strong force are the fundamental physical forces.
This classical theory of the electromagnetic field, introduced by the British physicist James Clerk Maxwell in 1864, is the precursor of gauge theories, although it was not until the early 20th century that the German mathematician Hermann Weyl developed the concept of gauge transformation entirely.
For general relativity theory, there is a major application of gage transformation. The transformation of the coordinate system is used in the transformation of the relativity gauge.The coordinate conversion is invertible, i.e. the reverse process should be done when the coordinate system is converted into another entity under a gage transformation.
Of electromagnetic theory, the gauge conversion is also being applied. The well-known electromagnetism equations, i.e. Maxwell’s formula can be converted by using meter transformation from one device to another. The Maxwell’s equations are invariant under the transformation of the gauge.