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Twistor Theory as an Approach to Fundamental Physics

  • Roger PenroseEmail author
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Abstract

The original motivations underlying the introduction of twistor theory are described, demanding a (3+1)-dimensional space-time theory dependent upon complex analysis and geometry. Space-time points are relegated to a secondary role, light rays, with a twisting aspect to them, being taken as more fundamental. The twistor treatment of wavefunctions for massless fields leads to a representation in terms of holomorphic sheaf cohomology. This, in turn, leads to a description of anti-self-dual (left-handed) gravitational (and Yang-mills) feeds. Failed attempts to remove this anti-self-dual restriction (the googly problem) led to a 40-year blockage to the development of twistor theory as a possible overall approach to fundamental physics. In recent years, a hopeful approach to deal with this problem—palatial twistor theory—has arisen, but the detailed development of these ideas has so far proved technically difficult.

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Notes

Acknowledgements

I’m grateful for Joseph Kouneiher, for his comments, suggestions throughout the process of writing and the preparation of this paper.

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Authors and Affiliations

  1. 1.Mathematical InstituteOxfordUK

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