DE-SITTER GAUGE-INVARIANCE AND DE-SITTER SPINOR CALCULUS IN GRAVITATION THEORY

In this paper I implement SO 2,3 gauge invariance in gravitation theory via the introduction of an auxiliary field χ A which represents the co-ordinates of the fibre in an associated bundle with the homogeneous space SO 2,3/SO 1,3 as standard fibre, SO 2,3 as 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 χ A (x). With this method I am able to reformulate MacDowell-Mansouri action in an explicitly SO 2,3-covariant form and also to find some solutions of this theory with nontrivial topology. Another SO 2,3-invariant action is also proposed. In the second part of the paper I discuss de Sitter spinor calculus introducing the spinor representation Sp 4, R of SO 2,3. The established spinor calculus enables me to rewrite the gravity actions in a fully de Sitter spinorial form which is the starting point for a generalization to a supersymmetric Osp 4/N spinor action which will be performed in a forthcoming paper. © 1979 Società Italiana di Fisica.