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

Author: Halpern L.  

Publisher: Springer Publishing Company

ISSN: 0020-7748

Source: International Journal of Theoretical Physics, Vol.40, Iss.1, 2001-01, pp. : 243-250

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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.