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Towards the geometrization of physics

Naturevolume 321pages417419 (1986) | Download Citation



The concept of symmetry breaking may be expressed mathematically by the reduction of a structure group, for example, choosing a point on a sphere reduces its symmetry group from the group of all rotations to the subgroup of rotations fixing that point. A systematic analysis of Penrose's twistor equation1,2 has revealed that twistor theory embodies a truth of nature: that interactive gravitational field theories in space-time correspond to such a symmetry breakdown—a breakdown that occurs, not in space-time, but in twistor space–the space of null geodesies of space-time. In particular, twistor theory lies at the heart of supergravity.

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  1. Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania, 15260, USA

    • George A. J. Sparling


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