  Local Lorentz transformations play an important role in teleparallel gravity
theories, in which a tetrad is conventionally employed as a fundamental field
variable describing the gravitational field. It is commonly understood that
modifications of general relativity in the teleparallel framework break a
certain notion of local Lorentz invariance, which is present in the pure tetrad
formulation of such theories, while another notion present in the covariant
formulation is preserved. We illuminate these different notions from a
geometric perspective, and distinguish them from what is commonly understood as
breaking of local Lorentz invariance in the context of gravity phenomenology.
Based on physical arguments, we present a geometric interpretation of the
dynamical fields in teleparallel gravity, which unified and refines the
conventional approaches.
