| Title: | THE TWISTOR APPROACH TO SPACE-TIME STRUCTURES |
| Source: | 100 YEARS OF RELATIVITY
Space-Time Structure: Einstein and Beyond (pp 465-505)
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| Author(s): | ROGER PENROSE
Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford OX1 3LB, UK
Institute for Gravitational Physics and Geometry, Penn State, University Park, PA 16802-6300, USA
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| Abstract: | An outline of twistor theory is presented. Initial motivations (from 1963) are given for this type of non-local geometry, as an intended scheme for unifying quantum theory and space-time structure. Basic twistor geometry and algebra is exhibited, and it is shown that this provides a complex-manifold description of classical (spinning) massless particles. Simple quantum commutation rules lead to a concise representation of massless particle wavefunctions, in terms of contour integrals or (more profoundly) holomorphic 1st cohomology. Non-linear versions give elegant representations of anti-self-dual Einstein (or Yang-Mills) fields, describing left-handed non-linear gravitons (or Yang-Mills particles). A brief outline of the current status of the ‘googly problem’ is provided, whereby the right-handed particles would also be incorporated. |
| Full Text: | View full text in PDF format (339KB) |
| TOC: | Back to Table of Contents |
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