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Teleparallel theory as a gauge theory of translations: Remarks and issues

M. Le Delliou, M. Fontanini

Abstract
The Teleparallel Equivalent to General Relativity (TEGR) is often presented as a gauge theory of translations, i.e., that uses only the translation group T4 = ( R4,+) as its gauge group. In a previous work we argued against this 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 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 arguments that originally led us to propose the Cartan connection in this context. This broadens the a priori possible choices for a TEGR connection.

Keywords
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Mathematical Physics

Physical Review D
Volume 101, Issue 0240, Page 5
2020 January

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Instituto de Astrofísica e Ciências do Espaço Universidade do Porto Faculdade de Ciências da Universidade de Lisboa
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia