Gauge gravitation theory: Gravity as a Higgs field

Sardanashvily, G.

doi:10.1142/s0219887816500869

Cited by 6 publications

(9 citation statements)

References 71 publications

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“…The curvature of the connection ω, as shown in Eq. (7), reduces to the torsion of the Lorentz connection if 1. ω L = ω W , the Weitzenbock connection, 2. the last term θ T ∧ ω L vanishes.…”

Section: Some Comments About the Connectionsmentioning

confidence: 99%

Teleparallel gravity equivalent of general relativity as a gauge theory: Translation or Cartan connection?

2019

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In this paper we question the status of TEGR, the Teleparallel Equivalent of General Relativity, as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group G: namely it does not present a mathematical structure underlying the theory which relates to a principal G-bundle and the choice of a connection on it (the gauge field). We point out that, while it is usually presented as absent, the gauging of the Lorentz symmetry is actually present in the theory, and that the choice of an Erhesmann connection to describe the gauge field makes the translations difficult to implement (mainly because there is in general no principal translation-bundle). We finally propose to use the Cartan Geometry and the Cartan connection as an alternative approach, naturally arising from the solution of the issues just mentioned, to obtain a more mathematically sound framework for TEGR.

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Section: Some Comments About the Connectionsmentioning

confidence: 99%

Teleparallel gravity equivalent of general relativity as a gauge theory: Translation or Cartan connection?

2019

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Section: Frame Bundle Reduction and Higgs Mechanismmentioning

confidence: 99%

“…In this section 7 , we discuss that the fiber bundle reduction can be in general viewed as the Higgs mechanism. In gravity theory at our hand, if we identify the vierbein as a Higgs field [7], the EOM (21) is naturally obtained. Let us start with summarizing the argument in Kobayashi and Nomizu's textbook [4] on how the principal bundle is reduced.…”

Section: Frame Bundle Reduction and Higgs Mechanismmentioning

confidence: 99%

“…6 From Eq. ( 25), one obtains the Riemannian tensor as 7 This section is new and not contained in the original Japanese version.…”

Section: Frame Bundle Reduction and Higgs Mechanismmentioning

confidence: 99%

“…By translating these known facts in mathematics into physics language, we may be able to explain the difference between general relativity and other gauge theories. This essentially corresponds to considering the first order formalism or Palatini formalism of general relativity [5,6,7], where we use the connection and vierbein as fundamental fields, rather than the metric.…”

Section: Introductionmentioning

confidence: 99%

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