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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Introduction to gauge theory

Maxwell’s equations can also be expressed in a generally covariant form, which is as invariant under general coordinate transformation as Einstein’s field equation. Mathematically, a gauge is just a choice of a local section of some principal bundle. Because the girls are identical, nobody jauhe be able to tell if they had been switched at birth; the labels A and B are arbitrary, and can be interchanged. In fact, a result in general gauge theory shows that affine representations i.

This is another example of a gauge transformation: For example, general nivariance states that gravitational fields have energy, and special relativity concludes that energy is equivalent to mass.

The fields remain the same under the gauge transformation, and therefore Maxwell’s equations are still satisfied. Retrieved from ” https: The set of possible gauge transformations of the entire configuration of a given gauge theory also forms a group, the gauge group of the theory. In other words, the distinguishing characteristic of a gauge theory is that the gauge field does not merely compensate for a poor choice of coordinate system; there is generally no gauge transformation that makes the gauge field vanish.

For a more accessible and less technical introduction to this topic, see Introduction to gauge theory.


Thus one could choose to define all voltage differences relative to some other standard, rather than the Earth, resulting in the addition of a constant offset. The nature of these particles is determined by the nature of the gauge transformations. However, in most gauge theories, there are many interesting questions which are non-perturbative.

One assumes an adequate experiment isolated from “external” influence that is itself a gauge-dependent statement. Now that it has been established that it is the potentials V and A that are fundamental, and not the fields E and Bwe can see that the gauge transformations, which change V and Ahave real physical significance, rather than being merely mathematical artifacts.

This new “derivative” is called a gauge covariant derivative and takes the jaugd. Recalling our two observers invariancd different ages: A gauge theory is a uauge of theory in physics. Gauge theories may be quantized by specialization of methods which are applicable to any quantum field theory.

Gauge theory

If there are no electric or magnetic fields present in this experiment, then the electron’s energy is constant, and, for example, there will be a high probability of detecting the electron along the central axis of the experiment, where by symmetry the two parts of the wave are in phase.

InAtiyah’s student Simon Donaldson built on this work to show that the differentiable classification of smooth 4- manifolds is very different from their classification up to homeomorphism. Gauge theories are usually discussed in the language of differential geometry. If there is a principal bundle P whose base space is space or spacetime and structure group is a Lie group, then the sections of P form a principal homogeneous space of the group of gauge transformations.

Technically, they reduce to the computations of certain correlation functions in the vacuum state. Generally, any theory that has the property of gauge invariance is considered a gauge theory.


University of Chicago Press: These transformations form a group of ” symmetries ” of the theory, and a physical situation corresponds not to an individual mathematical configuration but to a class of configurations related to one another by this symmetry group. Identifying the “charge” e not ivariance be confused with the mathematical constant e in the symmetry description with the usual electric charge this is the origin of the usage of the term in gauge theoriesand the gauge field A x with the four- vector potential of electromagnetic field results in an interaction Lagrangian.

Associated with any Lie group is the Lie algebra of group generators. According to the principles of quantum mechanics, particles do not actually invariamce trajectories through space.

Until the advent of quantum mechanics, the only well known example of gauge symmetry was in electromagnetism, and the general significance of the concept was not fully understood.

Although this cartoon ignores some technical details, it retains the physical phenomena that are important here.

Introduction to gauge theory – Wikipedia

But only differences in potential are physically measurable, which is the reason that a voltmeter must have two probes, and can only report the voltage difference between them. InChen Ning Yang and Robert Mills proposed to generalize these ideas to noncommutative groups. 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. This involves a renormalization of the theory.

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