The twistor approach to space-time structures

Details The twistor approach to space-time structures The twistor approach to space-time structures

Nov 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005yrst.book..465p&link_type=abstract

In: 100 years of relativity. Editor: Abhay Ashtekar. Singapore: World Scientific, ISBN 981-256-394-6, 2005, p. 465 - 505

Computer Science

Twistor Theory, Space-Time

Scientific paper

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.

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