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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Wikiquote has quotations related to: At present some of these methods lead to the most precise experimental tests of gauge theories. Because light from hydrogen atoms in distant galaxies may reach the earth after having traveled across space for billions of years, in effect one invadiance do such observations covering periods of time almost all the way jaauge to the Big Bangand they show that the laws of physics have always been the same.

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### Introduction to gauge theory – Wikipedia

History of quantum field theory Axiomatic quantum field theory Quantum field theory in curved spacetime. Associated with any Lie group is the Lie algebra of group generators. We cannot express the mathematical descriptions of the “setup information” and the “possible measurement outcomes”, or the “boundary conditions” of the invariamce, without reference to a particular coordinate system, including a choice of gauge.

Iinvariance are representations that transform covariantly pointwise called by physicists gauge transformations of the first kindrepresentations that transform as a connection form called by physicists gauge transformations of the second kind, an affine representation —and other more general representations, such as the B field in BF theory.

The earliest field theory having a gauge symmetry was Maxwell ‘s formulation, in —65, of electrodynamics ” A Dynamical Theory of the Electromagnetic Field “. Under such an infinitesimal gauge transformation.

Technically, they reduce to the computations of certain correlation functions in the vacuum state. This gauge theory, known as the Standard Modelaccurately describes experimental predictions regarding three of the four fundamental forces of nature. For instance, in Newtonian dynamicsif two configurations are related by a Galilean transformation an inertial change of reference frame they represent the same physical situation.

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## Gauge theory

Gauge symmetry is closely related to charge conservation. The main point to quantization is to be able to compute quantum amplitudes for various processes allowed by the theory.

A noncommutative gauge group can describe a field that, unlike the electromagnetic field, interacts with itself. However, to make this interaction physical and not completely arbitrary, the mediator A x needs to propagate in space. Historically, the first example of gauge symmetry to be discovered was classical electromagnetism.

Other examples of abelian groups are the integers under addition, 0, and negation, and the nonzero fractions under product, 1, and reciprocal. Also, for every phase there exists an inverse such that the sum of a phase and its inverse is 0. Two such mathematical configurations are equivalent describe the same physical situation if they are related by a transformation of this abstract coordinate basis a change of local section, or gauge transformation.

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.

Something in the theory must be changed. A gauge transformation is just a transformation between two such sections. The importance of gauge theories in physics is exemplified in the tremendous success of the mathematical formalism in providing a unified framework to describe the quantum field theories of electromagnetismthe weak force and the strong force.

The starting point of a quantum field theory is much like that of its continuum analog: Gauge theories constrain the laws of physics, because all the changes induced by a gauge transformation have to cancel each other out when written in terms of observable quantities.

In other words, the laws of physics governing electricity and magnetism that is, Maxwell equations are invariant under gauge transformation. More sophisticated quantum field theories, in particular those that involve a non-abelian gauge group, break the gauge symmetry within the techniques of perturbation theory by introducing additional fields the Faddeev—Popov ghosts and counterterms motivated by anomaly cancellationin an approach known as BRST quantization.

Today, gauge theories are useful in condensed matternuclear and high energy physics among other subfields. The fact that the symmetry is local means that we cannot even count on these proportions to remain fixed as the particles propagate through space. This was the first widely recognised gauge theory, popularised by Pauli in Other than these classical continuum field theories, the most widely known gauge theories are quantum field theoriesincluding quantum electrodynamics and the Standard Model of elementary particle physics.

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## Introduction to gauge theory

As a simple application of the formalism developed in the previous sections, consider the case of electrodynamicswith only the electron field. For each group generator there necessarily invxriance a corresponding field usually a vector field called the gauge field.

The gauge principle is therefore seen to naturally introduce the so-called minimal coupling of the electromagnetic field to the electron field. An alternative theory of gravitation, gauge theory gravityreplaces the principle of general covariance with a true gauge principle with new gauge fields. Consider a set of n non-interacting real scalar fieldswith equal masses m.

It is even possible to have cases in which an experiment’s results differ when the potentials are changed, even if no charged particle is ever exposed to a different field.

Gauge theories became even more attractive when it was realized that non-abelian gauge theories reproduced a feature called asymptotic freedom.

For an alternative formulation in terms of symmetries of the Lagrangian densitysee p. The transformations between possible gauges, called gauge transformationsform a Lie group—referred to as the symmetry group or the gauge group of the theory.

From Wikipedia, the free encyclopedia. The difference between this Lagrangian and the original globally gauge-invariant Lagrangian is seen to be the interaction Lagrangian. For example, if the double-slit experiment is performed with electrons, then a wave-like interference pattern is observed. Suppose that there existed some process by which one could briefly violate conservation of charge by creating a charge q at a certain point in space, 1, moving it to some other point 2, and then destroying it.

Mishandling gauge dependence calculations in boundary conditions is a frequent source of anomaliesand approaches to anomaly avoidance classifies gauge theories [ clarification needed ].

One assumes an adequate experiment isolated from “external” influence that is itself a gauge-dependent statement. Historically, the first example of gauge symmetry discovered was classical electromagnetism. There are more general nonlinear representations realizationsbut these are extremely complicated.