Letter: Some Remarks on the Coupling Prescription of Teleparallel Gravity

Mosna, Ricardo A.; Pereira, J. G.

doi:10.1023/b:gerg.0000046851.31889.7d

Cited by 28 publications

(27 citation statements)

References 17 publications

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“…Yang-Mills theories. In order to obtain the off-shell conserved currents we need to impose that both the gauge parameters and their derivatives vanish on the boundary 19 so that we obtain the set of identities:…”

Section: (Mdp)mentioning

confidence: 99%

The coupling of matter and spacetime geometry

Jiménez

Heisenberg

Koivisto

2020

Class. Quantum Grav.

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The geometrical formulation of gravity is not unique and can be set up in a variety of spacetimes. Even though the gravitational sector enjoys this freedom of different geometrical interpretations, consistent matter couplings have to be assured for a steady foundation of gravity. In generalised geometries, further ambiguities arise in the matter couplings unless the minimal coupling principle (MCP) is adopted that is compatible with the principles of relativity, universality and inertia. In this work, MCP is applied to all standard model gauge fields and matter fields in a completely general (linear) affine geometry. This is also discussed from an effective field theory perspective. It is found that the presence of torsion generically leads to theoretical problems. However, symmetric teleparallelism, wherein the affine geometry is integrable and torsion-free, is consistent with MCP. The generalised Bianchi identity is derived and shown to determine the dynamics of the connection in a unified fashion. Also, the parallel transport with respect to a teleparallel connection is shown to be free of second clock effects.

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Section: (Mdp)mentioning

confidence: 99%

The coupling of matter and spacetime geometry

Jiménez

Heisenberg

Koivisto

2020

Class. Quantum Grav.

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“…12.4.2, the gravitational interaction of a Dirac spinor ψ in Teleparallel Gravity involves only the vector and the axial parts of torsion [7]. In fact, in the class of frames in which the inertial connection vanishes, the teleparallel Dirac equation reads…”

Section: Looking For a Dual Gravitymentioning

confidence: 99%

Duality Symmetry

Aldrovandi¹,

Pereira²

2013

Teleparallel Gravity

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“…We will conclude with an application of the Kaluza-Klein tetrad Lagrangian (2. gives rise to both a Riemannian and a teleparallel structure on M." [46] For the usual Einstein-Maxwell-Dirac equations, in a non-compact four-dimensional space-time with spinor structure, the teleparallel covariant derivatives can be defined on the Kaluza-Klein manifold G X M × = with respect to the global moving frame ) , , (…”

Section: Theoremmentioning

confidence: 99%

Geometric Origin of Physical Constants in a Kaluza-Klein Tetrad Model

Reifler

Morris

2006

Found Phys Lett

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An important feature of Kaluza-Klein theories is their ability to relate fundamental physical constants to the radii of higher dimensions. In previous Kaluza-Klein theory, which unifies the electromagnetic field with gravity as dimensionless components of a Kaluza-Klein metric, i) all fields have the same physical dimensions, ii) the Lagrangian has no explicit dependence on any physical constants except mass, and hence iii) all physical constants in the field equations except for mass originate from geometry. While it seems natural in Kaluza-Klein theory to add fermion fields by defining higher dimensional bispinor fields on the Kaluza-Klein manifold, these Kaluza-Klein theories do not satisfy conditions (i), (ii), and (iii).In this paper, we show how conditions (i), (ii), and (iii) can be satisfied by including bispinor fields in a tetrad formulation of the Kaluza-Klein model, as well as in an equivalent teleparallel model. This demonstrates an unexpected feature of Dirac's bispinor equation, since conditions (i), (ii), (iii) imply a special relation among the terms in the Kaluza-Klein or teleparallel Lagrangian that would not be satisfied in general.

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Letter: Some Remarks on the Coupling Prescription of Teleparallel Gravity

Cited by 28 publications

References 17 publications

The coupling of matter and spacetime geometry

The coupling of matter and spacetime geometry

Duality Symmetry

Geometric Origin of Physical Constants in a Kaluza-Klein Tetrad Model

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