Understand
We demonstrate that from the first order formulation of the Einstein-Cartan action it is possible to derive the basic differential identity that leads to translational invariance of the action in the tangent space.
- The transformations of fields is written explicitly for both the first and second order formulations and the group properties of transformations are studied.
- This, combined with the preliminary results from the Hamiltonian formulation (arXiv:0907.1553 [gr-qc]), allows us to conclude that without any modification, the Einstein-Cartan action in any dimension higher than two possesses not only rotational invariance but also a form of \textit{translational invariance in the tangent space}.
- We argue that \textit{not} only a complete Hamiltonian analysis can unambiguously give an answer to the question of what a gauge symmetry is, but also the pure Lagrangian methods allow us to find the same gauge symmetry from the \textit{basic} differential identities.