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• Gauge_gravitation_theory abstract "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. It should not be confused with the related but distinct gauge theory gravity.The first gauge model of gravity was suggested by R. Utiyama 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. On the other hand, gravitation theory is built on the principal bundle of the tangent frames to . It belongs to the category of natural bundles for which diffeomorphisms of the base canonically give rise to automorphisms of . These automorphisms are called general covariant transformations. General covariant transformations are sufficient in order to restate Einstein's General Relativity and metric-affine gravitation theory as the gauge ones.In terms of gauge theory on natural bundles, gauge fields are linear connections on a world manifold , defined as principal connections on the linear frame bundle , and a metric (tetrad) gravitational field plays the role of a Higgs field responsible for spontaneous symmetry breaking of general covariant transformations.Spontaneous symmetry breaking is a quantum effect when the vacuum is not invariant under the transformation group. In classical gauge theory, spontaneous symmetry breaking occurs if the structure group of a principal bundle is reducible to a closed subgroup , i.e., there exists a principal subbundle of with the structure group . By virtue of the well-known theorem, there exists one-to-one correspondence between the reduced principal subbundles of with the structure group and the global sections of the quotient bundle . These sections are treated as classical Higgs fields.The idea of the pseudo-Riemannian metric as a Higgs field appeared while constructing non-linear (induced) representations of the general linear group , of which the Lorentz group is a Cartan subgroup. The geometric equivalence principle postulating the existence of a reference frame in which Lorentz invariants are defined on the whole world manifold is the theoretical justification of that the structure group of the linear frame bundle is reduced to the Lorentz group. Then the very definition of a pseudo-Riemannian metric on a manifold as a global section of the quotient bundle leads to its physical interpretation as a Higgs field. The physical reason for world symmetry breaking is the existence of Dirac fermion matter, whose symmetry group is the universal two-sheeted covering of the restricted Lorentz group, .".
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• Gauge_gravitation_theory subject Category:Gauge_theories.
• Gauge_gravitation_theory subject Category:Gravitation.
• Gauge_gravitation_theory subject Category:Theories_of_gravitation.
• Gauge_gravitation_theory type Abstraction100002137.
• Gauge_gravitation_theory type Cognition100023271.
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• Gauge_gravitation_theory type GaugeTheories.
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• Gauge_gravitation_theory type Theory105989479.
• Gauge_gravitation_theory type Thinking105770926.
• Gauge_gravitation_theory comment "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. It should not be confused with the related but distinct gauge theory gravity.The first gauge model of gravity was suggested by R. Utiyama in 1956 just two years after birth of the gauge theory itself.".
• Gauge_gravitation_theory label "Gauge gravitation theory".
• Gauge_gravitation_theory label "Teoría de norma gravitacional".
• Gauge_gravitation_theory label "Калибровочная теория гравитации".
• Gauge_gravitation_theory sameAs Teoría_de_norma_gravitacional.
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• Gauge_gravitation_theory wasDerivedFrom Gauge_gravitation_theory?oldid=600022297.
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