de Sitter gauge invariance and the geometry of the EinsteinCartan theory
Abstract
A formulation of general relativity as a gauge theory of the de Sitter group SO(3, 2) is used to analyse the geometrical structure of the EinsteinCartan theory. The SO(3, 2) symmetry must be spontaneously broken to the Lorentz group in order to reproduce the usual fourdimensional geometry of gravity. Special emphasis is placed upon the role of the Goldstone field of the symmetry breaking mechanism and also that of the original SO(3, 2) gauge fields. The latter are not directly identified with the gravitational vierbein and spin connection, but instead generate a kind of parallel transport known as development, which is the necessary construction to interpret the effects of spacetime torsion and curvature.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 August 1979
 DOI:
 10.1088/03054470/12/8/003
 Bibcode:
 1979JPhA...12L.205S
 Keywords:

 Einstein Equations;
 Gauge Invariance;
 Relativity;
 Cosmology;
 Gravitation Theory;
 Surface Geometry;
 Physics (General)