James D E Grant 1999 Class. Quantum Grav. 16 3419 doi:10.1088/0264-9381/16/11/301
A spinorial Hamiltonian approach to gravity
James D E Grant
Show affiliationsWe 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 dimensions, 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 
+, but such a reduction does not seem possible in dimensions 2 (mod 4), due to algebraic properties of spinors in these dimensions.
- PACS
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04.20.Cv Fundamental problems and general formalism
- MSC
- Subjects
- Dates
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Issue 11 (November 1999)
Received 22 December 1998, in final form 15 July 1999
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A spinorial Hamiltonian approach to gravity
James D E Grant 1999 Class. Quantum Grav. 16 3419
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