The twistor programme
Abstract
The formalism of twistors provides a new approach to the description of basic physics. The points of Minkowski spacetime are represented by 2dimensional linear subspaces of a complex 4dimensional vector space (flat twistor space) on which a Hermitian form of signature ++ is defined. Free massless fields can be represented in terms of the sheaf cohomology of portions of this space. Twistor space (or a suitable part of it) can be expressed in two different ways as a complex fibration. If one or the other fibration structure is deformed, the resulting space represents not empty Minkowski space but, in one case, the general "rightflat" solution of Einstein's vacuum equations and, in the other, the general (lefthanded) solution of Maxwell's equations. These provide the most primitive types of interaction (gravitational or electromagnetic) which may generalize to other fields in a comprehensive twistor scheme for the description of elementary particles.
 Publication:

Reports on Mathematical Physics
 Pub Date:
 August 1977
 DOI:
 10.1016/00344877(77)900477
 Bibcode:
 1977RpMP...12...65P