From Dirac's de Sitter Equation to a Generalization of Gravitational Theory

Abstract

Dirac's de Sitter covariant spinor wave equation, expressed on the group manifold of G = SO(3, 2) in terms of invariant vectors, gives rise to a modified Kaluza—Klein (KK) formalism with the Lorentz subgroup H = SO(3, 1) as typical fiber and the anti-de Sitter (AdS) space as base of the principal fiber bundle on G. The resulting gauge theory of gravitation gives an incomplete description of spinning particles because spin, considered as a generalized charge, has space-time properties. It is shown how the geometrical structure has to be altered to further modify the gauge formalism to a consistent theory of spin and gravitation. The resulting gravitational field equations on the bundle include torsion, and their projection on space-time is of higher nonlinearity in the curvature.