Research in Engineering and Aviation

Generalized Spinor Fields and Gravitation

March 1987

Author(s): Drechsler, W., Thacker, W.D.

Journal: Classical and Quantum Gravity, Vol. 4, pp. 291-318 (1987). DOI: 10.1088/0264-9381/4/2/012


The reduction of the gauge symmetry from the group G=SO(4,1) to the subgroup H=SO(3,1) is investigated in detail in a gauge theory based on the (4,1) de Sitter group, and the relation to the Lorentz gauge symmetry appearing in a vierbein formulation of gravity is pointed out. A key concept in this context is that of soldering and the related interlocked nature of the de Sitter frame bundle over spacetime with the ordinary Lorentz frame bundle over spacetime considered in a general relativistic framework. Generalised spinor fields Psi are introduced which transform under the non-linear realisation of G on the stability subgroup H of the origin in G/H, i.e. under the so-called SO(4,1)-Wigner rotations. The appearance of effects related to torsion in the dynamical equation for Psi is pointed out. The virtue of the present approach compared to the previous direct product formalism is that here the same spinor degrees of freedom transform, because of soldering, under both the internal de Sitter group and the spacetime Lorentz group.