Classical Gauge Gravitation Theory

Sardanashvily, G.

doi:10.1142/s0219887811005993

Cited by 12 publications

(33 citation statements)

References 30 publications

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“…A problem however is that that a non-linear (translation) summand of an affine connection (Section 12) is a soldering form, but neither frame (vierbein) field nor tetrad field. The latter thus has no the status of a gauge field [21,41,54]. At the same time, a translation part of an affine connection on R 3 characterizes an elastic distortion in gauge theory of dislocations in continuous media [23,32].…”

Section: Historymentioning

confidence: 99%

“…At the same time, gauge theory in a case of spontaneous symmetry breaking also contains classical Higgs fields, besides the gauge and matter ones [11,21,24,36,45,50,51,56,67]. Therefore, basing on the mathematical definition of a pseudo-Riemnnian metric, we have formulated gravitation theory as gauge theory with a Lorentz reduced structure where a metric gravitational field is treated as a Higgs field [11,21,40,44,49,54].…”

Section: Historymentioning

confidence: 99%

“…Gauge gravitation theory in comparison with the Yang-Mills one possesses the following peculiarities [11,54].…”

Section: Main Thesesmentioning

confidence: 99%

“…Gravitation theory on a world manifold X is formulated as gauge theory on natural bundles over X which admit general covariant transformations as the canonical functorial lift of diffeomorphisms of their base X [11,54]. This is metric-affine gravitation theory where gauge fields are general linear connections (Section 5), and a metric gravitational field is treated as a classical Higgs field responsible for reducing a structure group of natural bundles to a Lorentz group (Section 6).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Gauge gravitation theory: Gravity as a Higgs field

Sardanashvily

2016

Int. J. Geom. Methods Mod. Phys.

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Section: Historymentioning

confidence: 99%

Section: Historymentioning

confidence: 99%

“…Gauge gravitation theory in comparison with the Yang-Mills one possesses the following peculiarities [11,54].…”

Section: Main Thesesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Gauge gravitation theory: Gravity as a Higgs field

Sardanashvily

2016

Int. J. Geom. Methods Mod. Phys.

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“…However, these gauging approaches contain the problem with a non-linear (translation) summand of an affine connection being a soldering form, but neither a frame (vierbein) field nor a tetrad field. Thus the latter doesn't have the status of a gauge field [21][22][23]. At the same time, a gauge theory in the case of spontaneous symmetry breaking also contains classical Higgs fields, besides the gauge and matter ones [24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Dynamical symmetries, coherent states and nonlinear realizations: The SO(2,4) case

Arbuzov

Cirilo-Lombardo

2017

Int. J. Geom. Methods Mod. Phys.

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Nonlinear realizations of the SO(4, 2) group are discussed from the point of view of symmetries.Dynamical symmetry breaking is introduced. One linear and one quadratic model in curvature are constructed. Coherent states of the Klauder-Perelomov type are defined for both cases taking into account the coset geometry. A new spontaneous compactification mechanism is defined in the subspace invariant under the stability subgroup. The physical implications of the symmetry rupture in the context of non-linear realizations and direct gauging are analyzed and briefly discussed.

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Classical higgs fields

Sardanashvily

2014

Theor Math Phys

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We consider classical gauge theory on a principal bundle P → X in a case of spontaneous symmetry breaking characterized by the reduction of a structure group G of P → X to its closed subgroup H. This reduction is ensured by the existence of global sections of the quotient bundle P/H → X treated as classical Higgs fields. Matter fields with an exact symmetry group H in such gauge theory are considered in the pairs with Higgs fields, and they are represented by sections of a composite bundle Y → P/H → X, where Y → P/H is a fiber bundle associated to a principal bundle P → P/H with a structure group H. A key point is that a composite bundle Y → X is proved to be associated to a principal G-bundle P → X. Therefore, though matter fields possess an exact symmetry group H ⊂ G, their gauge G-invariant theory in the presence of Higgs fields can be developed. Its gauge invariant Lagrangian factorizes through the vertical covariant differential determined by a connection on a principal H-bundle P → P/H. In a case of the Cartan decomposition of a Lie algebra of G, this connection can be expressed in terms of a connection on a principal bundle P → X, i.e., gauge potentials for a group of broken symmetries G.

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Classical Gauge Gravitation Theory

Abstract: Classical gravitation theory is formulated as gauge theory on natural bundles where gauge symmetries are general covariant transformations and a gravitational field is a Higgs field responsible for their spontaneous symmetry breaking.

Cited by 12 publications

References 30 publications

Gauge gravitation theory: Gravity as a Higgs field

Gauge gravitation theory: Gravity as a Higgs field

Dynamical symmetries, coherent states and nonlinear realizations: The SO(2,4) case

Classical higgs fields

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