In quantum field theory, gauge gravitation theory is the effort to extend Yang–Mills theory, which provides a universal description of the fundamental interactions, to describe gravity.
Gauge gravitation theory should not be confused with the similarly-named gauge theory gravity, which is a formulation of (classical) gravitation in the language of geometric algebra. Nor should it be confused with Kaluza–Klein theory, where the gauge fields are used to describe particle fields, but not gravity itself.
The first gauge model of gravity was suggested by Ryoyu Utiyama (1916–1990) in 1956 just two years after birth of the gauge theory itself. However, the initial attempts to construct the gauge theory of gravity by analogy with the gauge models of internal symmetries encountered a problem of treating general covariant transformations and establishing the gauge status of a pseudo-Riemannian metric (a tetrad field).
In order to overcome this drawback, representing tetrad fields as gauge fields of the translation group was attempted. Infinitesimal generators of general covariant transformations were considered as those of the translation gauge group, and a tetrad (coframe) field was identified with the translation part of an affine connection on a world manifold . Any such connection is a sum of a linear world connection and a soldering form where is a non-holonomic frame. For instance, if is the Cartan connection, then is the canonical soldering form on . There are different physical interpretations of the translation part of affine connections. In gauge theory of dislocations, a field describes a distortion. At the same time, given a linear frame , the decomposition motivates many authors to treat a coframe as a translation gauge field.
Difficulties of constructing gauge gravitation theory by analogy with the Yang–Mills one result from the gauge transformations in these theories belonging to different classes. In the case of internal symmetries, the gauge transformations are just vertical automorphisms of a principal bundle leaving its base fixed.
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En physique théorique, une théorie de jauge est une théorie des champs basée sur un groupe de symétrie locale, appelé groupe de jauge, définissant une « invariance de jauge ». Le prototype le plus simple de théorie de jauge est l'électrodynamique classique de Maxwell. L'expression « invariance de jauge » a été introduite en 1918 par le mathématicien et physicien Hermann Weyl. La première théorie des champs à avoir une symétrie de jauge était la formulation de l'électrodynamisme de Maxwell en 1864 dans .
En géométrie différentielle, le groupe de jauge d'un fibré principal est le sous-groupe du groupe des automorphismes du fibré principal qui envoient ses fibres en elles-mêmes. La notion de groupe de jauge joue un rôle primordial en théorie de jauge. En particulier, son action de groupe sur un espace de formes de connexions donne lieu à la notion d'espace de module de connexions, nécessaire à la définition de l'homologie de Floer d'instantons. Soit un -fibré principal sur une variété différentielle et soit son action de groupe agissant par la droite.
In gravitation theory, a world manifold endowed with some Lorentzian pseudo-Riemannian metric and an associated space-time structure is a space-time. Gravitation theory is formulated as classical field theory on natural bundles over a world manifold. A world manifold is a four-dimensional orientable real smooth manifold. It is assumed to be a Hausdorff and second countable topological space. Consequently, it is a locally compact space which is a union of a countable number of compact subsets, a separable space, a paracompact and completely regular space.
The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions such as Quantum Electrodynamics.
Explore la théorie quantique des champs II, en mettant l'accent sur les théories de jauge, y compris la QED, les masses de fermion, les bosons vectoriels et le mécanisme de Higgs.
Explore les symétries de jauge dans la théorie quantique des champs, en mettant l'accent sur l'invariance sous les transformations et le rôle des champs fantômes.
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