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Old 13-07-2016, 11:32 AM
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sjastro
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For example, I still can’t comprehend why gauge theories are called “gauge”, but I understand (or at least I hope so) what the theories are about. You just have to be member of gang to speak their lingo properly
To understand the term gauge one needs to know about the mathematical concept of invariance and how this is applied to physics.
A simple example is rotating a triangle in Euclidean space.
The sum of the angles of the triangle will always equal 180 degrees irrespective of the rotation of the triangle in space.
In mathematical parlance the sum of the angles is invariant under a mathematical transformation involving rotation.
A gauge transformation is where invariance is preserved under that transformation.
The term gauge restricts the number of transformations possible.
For example in "uneven" (non isotropic) non Euclidean space the above example is clearly not a gauge transformation as the angles will always change as the triangle is rotated.

The idea can be extended to physics using classical electrodynamics as formulated by Maxwell.
The electromagnetic field can be expressed in terms of vector potentials.
It is found by applying a mathematical rotation results in a gauge transformation as the vector potentials remain invariant.

The obvious question is "so what?".
In the early 20th century before the advent of QM and at the dawn of GR it was found that electromagnetic and gravitational fields when described by a dynamical property known as a Lagrangian would generate the various conservation laws of physics under specific gauge transformations.

Modern day physics is built around this discovery.

The gauge bosons such as photons take the concept of gauge transformations further.
Not only must gauge transformations apply globally but to every individual point in space time.
These local gauge transformations result in the existence of massless bosons such as photons.
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