Gravitation as gauge theory of the diffeomorphism group

Cho, Y.M.; Soh, Kwang Sup; Yoon, Ji Hye; Park, Q-Han

doi:10.1016/0370-2693(92)91771-z

Cited by 39 publications

(56 citation statements)

References 16 publications

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“…The most general 4 + 4 decomposition of the 8D scalar curvature Geometric action was provided by [59] . Their main result is that m + n-dim Einstein gravity can be identified with an m-dimensional generally invariant gauge theory of Dif f s N , where N is an n-dim manifold.…”

Section: Gravity As Gauge Theories Of Diffs and Holograpymentioning

confidence: 99%

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

Castro

2005

Found Phys

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We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper and lower length scales (infrared/ultraviolet cutoff ). The invariance symmetry leads naturally to the real Clifford algebra Cl(2, 6, R) and complexified Clifford Cl C (4) algebra related to Twistors. We proceed with an extensive review of Smith's 8D model based on the Clifford algebra Cl(1, 7) that reproduces at low energies the physics of the Standard Model and Gravity; including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Further results by Smith are discussed pertaining the interplay among Clifford, Jordan, Division and Exceptional Lie algebras within the hierarchy of dimensions D = 26, 27, 28 related to bosonic string, M, F theory. Two Geometric actions are presented like the Clifford-Space extension of Maxwell's Electrodynamics, Brandt's action related the 8D spacetime tangent-bundle involving coordinates and velocities ( Finsler geometries ) followed by a discussion ( based on results by Cho et al ) why Einstein's gravity in m + n dimensions is equivalent to an m-dim Yang-Mills-like theory of diffemorphisms of an internal n-dim space which admits a holographic reduction to lower dimensions in the case of AdS m ×S n and dS m ×H n backgrounds. Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit.

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Section: Gravity As Gauge Theories Of Diffs and Holograpymentioning

confidence: 99%

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

Castro

2005

Found Phys

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“…Then, the Einstein's theory can be interpreted as a gauge theory defined on M 1+1 with diff(N 2 ) as a gauge symmetry, the diffeomorphism group of N 2 [3]. Let us introduce a coordinate system {u, v, y a : a = 2, 3} on E 4 , where {u, v} and {y a } are coordinates on M 1+1 and N 2 , respectively.…”

Section: Formalismmentioning

confidence: 99%

Quasilocal angular momentum of gravitational fields in (2+2) formalism

Yoon

2018

EPJ Web Conf.

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Abstract. Recently the Poisson algebra of a quasilocal angular momentum of gravitational fields L(ξ) in (2+2) formalism of Einstein's theory was studied in detail [1]. In this paper, we will briefly review the definition of L(ξ) and its remarkable properties. Especially, it will be discussed that, up to a constant normalizing factor, and this algebra reduces to the standard SO(3) algebra at null infinity. It will be also argued that our angular momentum is a quasilocal generalization of A. Rizzi's geometric definition. FormalismIn (2+2) formalism of Einstein's theory [2], the 4-dimensional spacetime E 4 is regarded as a fiber bundle that consists of a 2-dimensional base space M 1+1 of the Lorentzian signature and a 2-dimensional spacelike fiber N 2 at each point on M 1+1 . Then, the Einstein's theory can be interpreted as a gauge theory defined on M 1+1 with diff(N 2 ) as a gauge symmetry, the diffeomorphism group of N 2 [3]. Let us introduce a coordinate system {u, v, y a : a = 2, 3} on E 4 , where {u, v} and {y a } are coordinates on M 1+1 and N 2 , respectively. The most general line element is given by [4],All the metric components are functions of u, v, and y a , since we don't assume any spacetime isometry. Throughout this paper, the subscripts + and − denote u and v, respectively, and N 2 is assumed to be compact. The horizontal lifts∂ ± of the tangent vector fields ∂ ± are defined bŷwhere A a ± are the gauge connections of diff(N 2 ). The diff(N 2 )-covariant derivative of a diff(N 2 )-tensor density T ab··· cd··· with weight w is defined bywhere [A ± , T ] Lab··· cd··· denotes the Lie derivative of T ab··· cd··· with respect to A ± := A a ± ∂ a . It would be helpful to define the following in-and out-going null vector fields for understanding geometrical meanings of quasilocal angular momentum;

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“…Here R 2 is the scalar curvature of N 2 , and the diffN 2 -covariant derivatives are given by [8,10],…”

Section: Kinematicsmentioning

confidence: 99%

“…These reasonings led us to seek the possibility whether the Einstein's gravity in 3+1 dimensions without the self-dual restriction is describable as a 1+1 dimensional field theory [8]. The idea was simply to split a 3+1 dimensional spacetime into a 1+1 dimensional base manifold and a 2 dimensional fibre space, and write down the Einstein-Hilbert action.…”

Section: Introductionmentioning

confidence: 99%

New Hamiltonian formalism and quasilocal conservation equations of general relativity

Yoon

2004

Phys. Rev. D

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I describe the Einstein's gravitation of 3+1 dimensional spacetimes using the (2,2) formalism without assuming isometries. In this formalism, quasi-local energy, linear momentum, and angular momentum are identified from the four Einstein's equations of the divergencetype, and are expressed geometrically in terms of the area of a two-surface and a pair of null vector fields on that surface. The associated quasi-local balance equations are spelled out, and the corresponding fluxes are found to assume the canonical form of energy-momentum flux as in standard field theories. The remaining non-divergence-type Einstein's equations turn out to be the Hamilton's equations of motion, which are derivable from the nonvanishing Hamiltonian by the variational principle. The Hamilton's equations are the evolution equations along the out-going null geodesic whose affine parameter serves as the time function. In the asymptotic region of asymptotically flat spacetimes, it is shown that the quasi-local quantities reduce to the Bondi energy, linear momentum, and angular momentum, and the corresponding fluxes become the Bondi fluxes. The quasi-local angular momentum turns out to be zero for any two-surface in the flat Minkowski spacetime. I also present a candidate for quasi-local rotational energy which agrees with the Carter's constant in the asymptotic region of the Kerr spacetime. Finally, a simple relation between energy-flux and angular momentum-flux of a generic gravitational radiation is discussed, whose existence reflects the fact that energy-flux always accompanies angular momentum-flux unless the flux is an s-wave.

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Gravitation as gauge theory of the diffeomorphism group

Cited by 39 publications

References 16 publications

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

Quasilocal angular momentum of gravitational fields in (2+2) formalism

New Hamiltonian formalism and quasilocal conservation equations of general relativity

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