ar X iv : g r - qc / 9 81 20 50 v 1 1 5 D ec 1 99 8 A SPINORIAL HAMILTONIAN APPROACH TO RICCI - FLAT GEOMETRY II
نویسنده
چکیده
We give a spinorial set of Hamiltonian variables for General Relativity in any dimension greater than 2. This approach involves a study of the algebraic properties of spinors in higher dimension, and of the elimination of second-class constraints from the Hamiltonian theory. In four dimensions, when restricted to the positive spin-bundle, these variables reduce to the standard Ashtekar variables. In higher dimensions, the theory can either be reduced to a spinorial version of the ADM formalism, or can be left in a more general form which seems useful for the investigation of some spinorial problems such as Riemannian manifolds with reduced holonomy group. In dimensions 0 (mod 4), the theory may be recast solely in terms of structures on the positive spin-bundle V + , but such a reduction does not seem possible in dimensions 2 (mod 4), due to algebraic properties of spinors in these dimensions.
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تاریخ انتشار 1998