Teleparallel gravity from the principal bundle viewpoint

A bstract We examine whether the Teleparallel Equivalent of General Relativity (TEGR) can be formulated as a gauge theory in the language of connections on principal bundles. We argue in favor of using either the affine bundle with the Poincaré group or, equivalently, the orthonormal frame bundle with the Lorentz group as the structure group. Following the framework of Trautman — where gauge symmetries are determined using the absolute elements — we set to identify the absolute elements and gauge symmetries of TEGR. The triviality of the field equations for metric teleparallel connection raises the question of whether it should be treated as a dynamical variable. If the connection is treated as dynamical, then the only absolute element is the canonical 1-form of the frame bundle, and the gauge group of TEGR is the full diffeomorphism group. If the connection is considered as non-dynamical, we show that its treatment as an absolute element leads to problems of not being able to determine the gauge group and its possible non-uniqueness. On the other hand, if the connection is treated as a non-dynamical variable but not as an absolute element, we again recover the whole diffeomorphism group as the gauge group of TEGR.