2018/11/09 by Michele Fontanini, M Fontanini, E. Huguet +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #BRST quantization #Black Holes and Theoretical Physics #Computer science #Connection (principal bundle) #Cosmology and Gravitation Theories #Gauge (firearms) #Gauge anomaly #Gauge covariant derivative #Gauge symmetry #Gauge theory #General relativity #Geometry #Introduction to gauge theory #Lorenz gauge condition #Mathematical physics #Mathematics #Physics #Principal (computer security) #Symmetry (geometry) #Theoretical physics #Theory of relativity #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.99.064006
published as Phys. Rev. D 99, 064006 (2019) · 12pp, 8 figs
arxiv created 2018/11/09 · openalex created_date 2018/11/16 · openalex publication_date 2019/03/06 · arxiv updated 2019/03/13 · openalex updated_date 2026/08/05
In this paper we question the status of TEGR, the Teleparallel Equivalent of General Relativity, as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group G: namely it does not present a mathematical structure underlying the theory which relates to a principal G-bundle and the choice of a connection on it (the gauge field). We point out that, while it is usually presented as absent, the gauging of the Lorentz symmetry is actually present in the theory, and that the choice of an Erhesmann connection to describe the gauge field makes the translations difficult to implement (mainly because there is in general no principal translation-bundle). We finally propose to use the Cartan Geometry and the Cartan connection as an alternative approach, naturally arising from the solution of the issues just mentioned, to obtain a more mathematically sound framework for TEGR.