A Brief Guide to Variations in Teleparallel Gauge Theories of Gravity and the Kaniel-Itin Model

Muench, Uwe; Gronwald, Frank; Hehl, Friedrich W.

doi:10.1023/a:1026616326685

Cited by 50 publications

(89 citation statements)

References 22 publications

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“…Here we need the master formula of [8] for the commutator of a variation δ with the Hodge star operator ⋆ . The energy-momentum is still tracefree as in Maxwell's theory,…”

Section: Energy-momentummentioning

confidence: 99%

An Assessment of Evans’ Unified Field Theory II

Hehl

Obukhov

2007

Found Phys

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Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans' theory and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation, together with Evans' unified field theory, collapses to an ordinary Einstein equation.

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“…Here we need the master formula of [8] for the commutator of a variation δ with the Hodge star operator ⋆ . The energy-momentum is still tracefree as in Maxwell's theory,…”

Section: Energy-momentummentioning

confidence: 99%

An Assessment of Evans’ Unified Field Theory II

Hehl

Obukhov

2007

Found Phys

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“…20 The idea was later picked up and developed into a full-fledged gauge theory of gravity (cf. Hayashi & Shirafuji 1979;Muench et al 1998). It turns out --details aside --that the Weitzenböck spacetime has enough geometry of the right kind to describe gravity.…”

Section: Gauge Theories Of Gravitymentioning

confidence: 99%

Gauge gravity and the unification of natural forces

Liu

2003

International Studies in the Philosophy of Science

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“…It can be constructed as a linear combination of three Weitzenböck quadratic teleparallel invariants [3]. The symmetric form of this Lagrangian is [26] …”

Section: The Energy-momentum Tensormentioning

confidence: 99%

“…Some of them are known to be applicable for description of the gravitational field. The field equation is derived from the Lagrangian (38) in the form [17], [26] …”

Section: The Energy-momentum Tensormentioning

confidence: 99%

“…The standard computations of the variation of a Lagrangian defined on a teleparallel manifold are rather complicated. It is because one needs to vary not only the coframe ϑ a itself, but also the the dual frame e a and even the Hodge dual operator, that depends on the coframe implicitly [26]. In order to avoid these technical problems we will rewrite the total Lagrangian (45) in a compact form which will be useful for the variation procedure.…”

Section: A the Total Lagrangianmentioning

confidence: 99%

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Conserved Current for General Teleparallel Models

Itin

2002

Int. J. Mod. Phys. A

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The obstruction for the existence of an energy momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. It has not to be valid for alternative geometrical structures. A teleparallel manifold is defined as a parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields related by global Lorentz, i.e., SO(1, 3) transformations. In this article a general 3-parameter class of teleparallel models is considered. It includes a 1-parameter subclass of models with the Schwarzschild coframe solution (generalized teleparallel equivalent of gravity). A new form of the coframe field equation is derived here from the general teleparallel Lagrangian by introducing the notion of a 3-parameter conjugate field strength F a . The field equation turns out to have a form completely similar to the Maxwell field equation d * F a = T a . By applying the Noether procedure, the source 3-form T a is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source of the coframe field is interpreted as the total conserved energymomentum current of the system. A reduction of the conserved current to the Noether current and the Noether charge for the coframe field is provided. The energy-momentum tensor is defined as a map of the module of current 3-forms into the module of vector fields. Thus an energy-momentum tensor for the coframe field is defined in a diffeomorphism invariant and a translational covariant way. The total energy-momentum current of a system is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) field is possible in principle, unlike as in GR. The energy-momentum tensor is calculated for various teleparallel models: the pure Yang-Mills type model, the anti-Yang-Mills type model and the generalized teleparallel equivalent of GR. The latter case can serve as a very close alternative to the GR description of gravity.

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A Brief Guide to Variations in Teleparallel Gauge Theories of Gravity and the Kaniel-Itin Model

Cited by 50 publications

References 22 publications

An Assessment of Evans’ Unified Field Theory II

An Assessment of Evans’ Unified Field Theory II

Gauge gravity and the unification of natural forces

Conserved Current for General Teleparallel Models

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