Description
It is well known that the Teleparallel Equivalent of General Relativity (TEGR) is locally dynamically equivalent to General Relativity in the absence of matter. However, for decades, discussions have persisted about this equivalence when matter is present. These discussions primarily focus on the choice of coupling prescription, whether to use the metric teleparallel or the Levi-Civita one, and the description of spinor fields.
In this talk, we address the situation with coupling prescriptions and spinor fields in TEGR. Using Noether's second theorem, we argue that the structure of Noether's identities in TEGR results in the Levi-Civita coupling. As a consequence, one can consistently describe spinor fields in TEGR. Moreover, Noether's identities also allow us to analyze the gauge structure of TEGR and the popular claim that TEGR can be viewed as a gauge theory of translations. We explain that the gauge symmetries in TEGR are diffeomorphisms and local Lorentz transformations, and that no (internal) translational gauge symmetry is present.