Teleparallel gravity equivalent of general relativity as a gauge theory: Translation or Cartan connection?
Abstract
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 translationgauge 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 translationbundle). 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.
 Publication:

Physical Review D
 Pub Date:
 March 2019
 DOI:
 10.1103/PhysRevD.99.064006
 arXiv:
 arXiv:1811.03810
 Bibcode:
 2019PhRvD..99f4006F
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 12pp, 8 figs