In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations. The term gauge refers to. quatrième section, j’aborderai le rôle de la symétrie de jauge dans la procédure entités de la théorie) sur l’espace-temps4, l’invariance de jauge implique. “Optique Géométrique et invariance de jauge: Solutions oscillantes d’amplitude critique pour les équations de Yang-Mills.” Séminaire Équations aux dérivées.
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But there are two entirely different reasons that the waves could have changed.
Gauge theory – Wikipedia
In quantum mechanics, a particle such as an electron is also described as a wave. There is one conserved current for every generator.
This motivated searching for a strong force gauge theory. Surprisingly, gauge symmetry can give a deeper explanation for the existence of interactions, such as the electric and nuclear interactions. The nature of these particles is determined by the nature of the gauge transformations.
They could have changed because they uauge oscillating with a certain wavelength, or they could have changed because the gauge function changed from a mixture to, say, Theories of quantum gravitybeginning with gauge gravitation theoryalso postulate the existence of a gauge boson known as the graviton. The results of the experiment will be different, because phase relationships between the two parts of the electron wave have changed, and therefore the locations of constructive and destructive interference will be shifted to one side or the other.
Its case is somewhat unusual in that the gauge field is a tensor, the Lanczos tensor. jaige
Historically, the first example of gauge symmetry discovered was classical electromagnetism. In addition to its interaction with other objects via the covariant derivative, the gauge field typically contributes energy in the form of jage “self-energy” term.
Not only that, but it is not even necessary to change the speed of each clock by invarianfe fixed amount. For example, if the double-slit experiment is performed with electrons, then a wave-like interference pattern is observed. The main point to quantization is to be able to compute quantum amplitudes for various processes allowed by the theory.
We cannot express the mathematical descriptions of the “setup information” and the “possible measurement outcomes”, or the “boundary conditions” of the experiment, without reference to a particular coordinate system, including a choice invarinace gauge.
One can obtain the equations for the gauge theory by:. The Strange Theory of Light and Matter. The Gupta—Bleuler method was also developed to handle this problem.
Introduction to gauge theory – Wikipedia
A noncommutative gauge group can describe a field that, unlike the electromagnetic field, interacts with itself. Inattempting to resolve some of the great confusion in elementary particle physicsChen Ning Yang and Robert Mills introduced non-abelian gauge invafiance as models to understand the strong interaction holding together nucleons in atomic nuclei.
The jquge field theory having a gauge symmetry was Maxwell ‘s formulation, in —65, of electrodynamics ” A Dynamical Theory of the Electromagnetic Field ” which stated that any function whose curl vanishes—and can therefore normally be written as a gradient —could be added to the vector potential without dd the magnetic field.
Hence a gravitational field induces a further gravitational field. Where g is called the coupling constant; a quantity defining the strength of an interaction. Gauge symmetries can be viewed as analogues of the principle of general covariance of general relativity in which the coordinate system can be chosen freely under arbitrary diffeomorphisms of spacetime. Standard Model Quantum electrodynamics Electroweak interaction Quantum chromodynamics Higgs mechanism.
Similarly unnoticed, Hilbert had derived the Einstein field equations by postulating the invariance of the action under a general coordinate transformation. The conclusion is that if gauge symmetry holds, and energy is conserved, then charge must be conserved.
This idea can be generalized to include local as well as global symmetries, analogous to much more abstract “changes of coordinates” in a situation where there is no preferred ” inertial ” coordinate system that covers the entire physical system.
A gauge transformation is just a transformation between two such sections. The result is that we have an explanation for the presence of electromagnetic interactions: An element of the gauge group can be parameterized by a smoothly varying function from the points of spacetime to the finite-dimensional Lie group, such that the value of the function and its derivatives at each point represents the action of the gauge transformation on the fiber over that point.
A transformation from one such field configuration to another is called a gauge transformation ;   the lack of change in the measurable quantities, despite the field being transformed, is a property called gauge invariance. There are more general nonlinear representations realizationsbut these are extremely complicated.
In general, such particles are called gauge bosonswhere the term “boson” refers to a particle with integer spin.