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Two-spinor formulation of first-order gravity coupled to Dirac fields. (English) Zbl 0976.83037

The authors develop a 2-component formalism for the splitting of the Einstein Lagrangian which is applicable to any \(4m\)-dimensional differentiable manifold admitting a pseudo-Riemannian metric of arbitrary signature without imposing any stringent topological requirements such as parallelizability. This is then applied to first-order gravity theory coupled with Dirac fields. Contents includes: an introduction; spin structures, spin-frames, and soldering forms; standard general relativity in the two-spinor formalism; and the global first-order spinor Einstein Lagrangian. The paper concludes with a 41 item list of references.

MSC:

83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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