Teleparallel theory as a gauge theory of translations: comments and issues
arXiv:1910.08471 · doi:10.1103/PhysRevD.101.024059
Abstract
The Teleparallel Equivalent to General Relativity (TEGR) is often presented as a gauge theory of translations, i.e., that uses \emph{only} the translation group $T_4 = (\setR^4, +)$ as its gauge group. In a previous work we argued against this \emph{translation-only} formalism on the basis of its mathematical shortcomings. We then provided an alternative proposal using a Cartan connection. Recently, a reply by some of the authors defending TEGR as a \emph{translation-only} gauge theory discussed our objections. Here, we first clarify our arguments, and give new proofs of some statements, to answer to these discussions, maintaining our first claim. We then amend one of the argument that originally led us to propose the Cartan connection in this context. This broadens the \emph{a priori} possible choices for a TEGR connection.
arXiv comment5pp, RevTeX4.1
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Cited by in corpus (10)
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- General relativity as a special case of Poincaré gauge gravity
- Teleparallel gravity as a gauge theory: coupling to matter with Cartan connection
- Cartan approach to Teleparallel Equivalent to General Relativity: a review
- Gauging the higher-spin-like symmetries by the Moyal product
- Tangent space symmetries in general relativity and teleparallelism
- The meaning of torsion in teleparallel theories
- Focusing conditions for extended teleparallel gravity theories
- Conservation laws in gauge gravity theory
- Minisuperspace Cosmology in Extended Geometric Trinity of Gravity