2009/07/31 by N. Kiriushcheva, S. V. Kuzmin · 7 citations
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential geometry #Einstein #Gauge symmetry #Gauge theory #Geometry #Hamiltonian (control theory) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Rotational invariance #Symmetry (geometry) #Tangent space #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1007/s10714-010-1003-7
published in General Relativity and Gravitation 42(11), 2613-2631 (Springer Science+Business Media) · 25 pages, new Section on group properties of transformations is added, references are added. This version will appear in General Relativity and Gravitation
arxiv created 2010/05/18 · openalex publication_date 2010/05/19 · arxiv updated 2011/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 translational invariance in the tangent space. We argue that 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 basic differential identities.