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A Spinorial Hamiltonian Approach to Gravity

Grant, JDE (1998) A Spinorial Hamiltonian Approach to Gravity Classical and Quantum Gravity, 16. pp. 3419-3437.

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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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 15 December 1998
DOI : 10.1088/0264-9381/16/11/301
Uncontrolled Keywords : gr-qc, gr-qc, hep-th
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 13:28
Last Modified : 11 Jun 2019 09:52

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