Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979ncimb..53..369f&link_type=abstract
Nuovo Cimento B, Serie 11, vol. 53 B, Oct. 11, 1979, p. 369-384. Research supported by the Rotary Foundation.
Astronomy and Astrophysics
Astronomy
4
Cosmology, Gauge Invariance, Gravitation Theory, Relativity, Astronomical Models, Equations Of Motion, Spinor Groups, Vector Analysis
Scientific paper
The paper implements the SO(2,3) gauge invariance in the gravitation theory by introducing an auxiliary field chi(A) which represents the coordinates of the fiber in an associated bundle with homogeneous space SO(2,3)/(SO(1,3) as the standard fiber, SO(2,3) as a structural group, and space-time as a base space. The usual vierbeins are interpreted as a set of four orthogonal 1-form vectors in the plane orthogonal to the vector chi(A)(x). The MacDowell-Mansouri action is reformulated in an explicitly SO(2,3)-covariant form, and solutions found for this theory with nontrivial topology. The de Sitter spinor calculus is discussed in the second part of the paper, and this calculus makes possible rewriting the gravity actions in a fully de Sitter spinorial form from which a generalization to a supersymmetric spinor action will be presented in a forthcoming paper.
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