We question the status of TEGR, the Teleparallel Equivalent of General Relativity,
as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group G: namely it does not present
a mathematical structure underlying the theory which relates to a principal G-bundle and the choice of a connection on it (the gauge field). We point out that, while it is usually presented as absent, the gauging of the
Lorentz symmetry is actually present in the theory, and that the choice of an Erhesmann connection
to describe the gauge field makes the translations difficult to implement. We finally propose to use the Cartan Geometry and the Cartan connection as an alternative approach.
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