de Sitter gauge invariance and the geometry of the Einstein-Cartan theory

Details de Sitter gauge invariance and the geometry of the Einstein-Cartan theory de Sitter gauge invariance and the geometry of the Einstein-Cartan theory

Aug 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979jpha...12l.205s&link_type=abstract

Journal of Physics A - Mathematical and General, vol. 12, Aug. 1979, p. L205-L210. Science Research Council

Physics

9

Einstein Equations, Gauge Invariance, Relativity, Cosmology, Gravitation Theory, Surface Geometry

Scientific paper

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 Einstein-Cartan theory. The SO(3, 2) symmetry must be spontaneously broken to the Lorentz group in order to reproduce the usual four-dimensional 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 space-time torsion and curvature.

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