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arXiv · 2008.13493

Teleparallel gravity as a gauge theory: coupling to matter with Cartan connection

E. Huguet·M. Le Delliou·M. Fontanini·Z. -C. Lin
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Abstract

We present a consistent and complete description of the coupling to matter in the Teleparallel Equivalent to General Relativity (TEGR) theory built from a Cartan connection, as we proposed in previous works. A first theorem allows us to obtain parallel transport from the Cartan connection into a proper Ehresmann connection, while a second ensures to link the TEGR-Cartan connection to the Ehresmann one-form that contains the Levi-Civita connection. This yields a coupling to matter in agreement with observations and the Equivalence Principle. As the fundamental fields proceed from the Cartan connection, if one insists on interpreting TEGR as a gauge theory of translations, such translation gauge field can be extracted from the consistent theory presented. However, this would entail a fundamental change in the structures known for gauge theory and a split between gauge field and connection is imperative. The willingness to take such a step is left to the reader.

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E. Huguet, M. Le Delliou, M. Fontanini, Z. -C. Lin. 2020-08-31. Teleparallel gravity as a gauge theory: coupling to matter with Cartan connection. https://doi.org/10.1103/physrevd.103.044061

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