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2019

First-order formulation of teleparallel gravity and dual loop gravity

Dupuis, Maïté, Girelli, Florian, Osumanu, Abdulmajid et al.

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There are at least two ways to encode gravity into geometry: Einstein's general theory of relativity (GR) for the metric tensor, and teleparallel gravity, where torsion as opposed to curvature encodes the dynamics of the gravitational degrees of freedom.

The main purpose of the paper is to explore the relation between loop gravity and teleparallel gravity.
We argue that these two formulations of gravity are related to two different discretizations of the Einstein--Cartan action, which were studied recently in the literature.
The first discretization leads to the \emph{{loop gravity}} kinematical phase space where the zero torsion condition is enforced {first} and the other is the \emph{{dual loop gravity}} kinematical phase space where curvature is imposed to vanish {first}.

First-order formulation of teleparallel gravity and dual loop gravity · Around

Built on

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J. M. Nester and H.-J. Yo, “Symmetric teleparallel general relativity,” Chin. J. Phys
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Then

B. Dittrich and M. Geiller, “A new vacuum for Loop Quantum Gravity,” Class. Quant. Grav
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2015
Later among the works it cites.
A. Golovnev, T. Koivisto, and M. Sandstad, “On the covariance of teleparallel gravity theories,” Class. Quant. Grav
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2017
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M. Dupuis, L. Freidel, and F. Girelli, “Discretization of 3d gravity in different polarizations,” Phys. Rev
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P. Tiede, “The Relation between Polygonal Gravity and 3D Loop Quantum Gravity,” Master’s thesis, Waterloo U., Math. Dept., 2017
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B. Dittrich and M. Geiller, “Quantum gravity kinematics from extended TQFTs,” New J. Phys
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B. Dittrich and M. Geiller, “Flux formulation of loop quantum gravity: Classical framework,” Class. Quant. Grav

2015

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L. Heisenberg, “A systematic approach to generalisations of General Relativity and their cosmological implications,” arXiv:1807.01725 [gr-qc]

Cited in the paper.

C. Delcamp, L. Freidel, and F. Girelli, “Dual canonical quantization of 3D quantum gravity,”. In preparation

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2017

Later among the works it cites.

L. Freidel, F. Girelli, and B. Shoshany, “2+1D Loop Quantum Gravity on the Edge,” Phys. Rev

2019

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