A Spinorial Hamiltonian Approach to Gravity

Details A Spinorial Hamiltonian Approach to Gravity A Spinorial Hamiltonian Approach to Gravity

1998-12-15

arxiv.org/abs/gr-qc/9812050v2

Classical and Quantum Gravity 16, 3419--3437 (1999)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, Latex 2e. Published version

Scientific paper

10.1088/0264-9381/16/11/301

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 $0 \pmod 4$, the theory may be recast solely in terms of structures on the positive spin-bundle $\mathbb{V}^+$, but such a reduction does not seem possible in dimensions $2 \pmod 4$, due to algebraic properties of spinors in these dimensions.

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