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The generalized Penrose-Ward transform

Published online by Cambridge University Press:  24 October 2008

Michael G. Eastwood
Michael G. Eastwood
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford 0X1 3LB
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Extract

The Penrose transform is an integral geometric method of interpreting elements of various analytic cohomology groups on open subsets of complex projective 3-space as solutions of linear differential equations on the Grassmannian of 2-planes in 4-space. The motivation for such a transform comes from interpreting this Grassmannian as the complexification of the conformal compactification of Minkowski space, the differential equations being the massless field equations of various helicities. This transform is a cornerstone of twistor theory [22, 24, 30], but the methods generalize considerably as will be explained in this article. Closely related is the Ward correspondence[28], a non-linear version of a special case of the Penrose transform. It also admits a rather more general treatment. The object of this article is to explain the general case and the natural connection between the Penrose and Ward approaches.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 165 - 187
Copyright
Copyright © Cambridge Philosophical Society 1985

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